Publication Awards

2004 Outstanding Article Publication Award, ASA Mathematical Sociology Section, for "Structural Cohesion and Embeddedness: A Hierarchical Concept of Social Groups" - Moody and White (2003, below) cited in Annual Review of Sociology 2004

2007 Best Article Award, ASA Economic Sociology Section, for "Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings" - Powell, White, Koput, and Owen-Smith (2005, below)

2007 selected as a 2008 'Highlight' paper of The European Physical Journal B 60: "Role Models for Complex Networks - Joerg Reichardt and Douglas R. White (2007, below). Santa Fe Institute working papers.

Chapters in Handbooks and Encyclopedias in PDF format, including those in press

2011 Douglas R. White. Download: Chapter 10: Kinship, Class, and Community. In John C. Scott and Peter Carrington, Eds., pp129-147. Sage Handbook of Social Networks. Chapter Authors. early draft. Preprinted at Santa Fe Institute Working Paper 11-04-015. Preprint at World Cultures eJournal 18(2): article 2. 30pp. Preprint at Paul L. Lazarsfeld Center, Columbia University.

Abstract. This review presents studies in various world regions. Each uses network analysis software designed explicitly for kinship studies with explicit network measures of cohesion. It presents evidence of fundamental differences in the forms of marital cohesion that show profoundly different effects over a wide range of social phenomena, regional scales, and diverse cultures. Social cohesion is the basis of mutuality, cooperation and well-being in human societies (Council of Europe, 2009). It includes the modes by which people are assimilated into societies, how groups hold power, stratify social relations, and manage the flow of resources. Kinship networks in the civil societies of nation-states, in contrast to smaller-scale societies, are far too rarely studied as a basis of social cohesion. Networks, the social tissues of our lives, are only partially visible to us; thus we fail to see how these are wrapped and embedded in larger networks. Thus the importance, as emphasized here, of an explicit science of social network analysis for kinship studies both at local and larger scales. The analyses of cohesive subsets show how constructions of social class, ethnicity, migration, inheritance, social movements, and other large- as well as small-scale social phenomena are implicated in kinship networks.

2011 Klaus Hamberger, Michael Houseman, Douglas R. White. Download: Chapter 35: Kinship Network Analysis. In John C. Scott and Peter Carrington, Eds., pp533-549. Sage Handbook of Social Networks.








Abstract. Abstract for another article by White and Houseman forthcoming in L'homme. This chapter focuses on substantive findings and network methods resulting from the weaving together of anglophone and the francophone social science traditions dealing with kinship. The merger of these two traditions has dealt with kinship networks as research objects using P-systems. P-systems include graph theoretic network approaches as formal methods for analyzing relations of parentage and the larger units (marriages, kin groups, cohesive groups) in which individuals are embedded. Harary and White (2001) provide a summary formulation, just as White and Harary (2001) provide new foundations for the study of cohesion, which apply also to kinship networks. The first of these approaches trace back to the field of kinship computing, partly inspired by the works of mathematicians Andre´ Weil (1949) and Oystein Ore (1960), as established by P-graph analysis of kinship networks (White and Jorion 1992) and then incorporated into Pajek (Batagelj and Mrvar 1998, White, Batagelj, and Mrvar 1999) and other software, most recently, Hamberger and Houseman (2008), Hamberger, Houseman and Grange( 2008), Hamberger and Daillant (2009). P-systems incorporate models of kinship through relations of coupling and parentage, with graphs embedded within the nodes of other graphs, and segregation of higher level descent and marriage structure from nuclear family structure. White and Johansen (2006) view these contrasting perspectives as embodying the key conceptual distinction used by Lévi-Strauss (1949) in the theory of marriage alliance and by Murdock (1949) in a theory that views kinship as an extension of the family. P-systems endorse neither theory, and are generally neutral with respect to favored theories. Rather, they allow a synthesis of key elements of many different theoretical approaches, including those of complex systems. "While a P-system is used to represent a concrete network of kinship and marriage relationships, this network also constitutes a system in the sense that it contains multiple levels where each level is a graph in which each node contains another graph structure. In sum, the connections between the nodes at the outer level in a P-system are especially useful in the analysis of marriage and descent, while at inner level we can describe how individuals are embedded in the kinship structure" (Harary and White 2001:1). Kinship computing has contributed a wide range of substantive contributions that are reviewed here. These approaches have produced new substantive results in sociology, history, ethnography, and SNA with its development of the new field of kinship computing inaugurated in White and Jorion (1992).

click 2011 Douglas R. White. Download: Chapter 18: Social Networks, Cognition and Culture. In David Kronenfeld, Giovanni Bennardo, Victor De Munch, and Michael Fischer, Eds., pp331-354 Blackwell Companion to Handbook of Cognitive Anthropology. Table of Contents. UCSD e-access. Author draft 2010. DRW Abstract#54. Appendices to Social Networks, Cognition and Culture. Afterthoughts 2011 on Fig. 1.

Abstract. Three theories new to cognitive anthropology are proposed and either tested or supported with empirical evidence. First, predictive cohesion theory suggests the cohesion-consensus hypothesis of cultural sharing. Structural cohesion is a formal network measure that identifies the group boundaries for which the redundancy or multiconnectivity of ties is greatest and a group is least likely to be separated. It is thus an identifier of groups within which culture is most likely to be shared.

Second, ecological psychology suggests that the way perceptions are stored episodically in memory lends itself to network coding of links representing people and interactions: multiple dyadic bonds at a temporal scale of experiential events and contexts. Kinship networks, for example, can be drawn to represent a more macro time scale of dyads and events such as marriage, childbirth, death, migration, and proximal interactions. At this scale there are culturally recognized and individually perceived event boundaries and time-scales of event sequences but other contexts that have different times-scales and event sequences.

Third, research on animal and primate perceptions suggest that the information processing capacities of humans are exceptional in the perception of event and interaction structures such as might be coded for different aspects of social network interactions and contexts. Elements of network structure may thus be perceived or experienced (as with membership in a structrually cohesive group) and have causal efficacy without necessarily being named entities. Taken together, these theoretical viewpoints provide new approaches to study of the relation between social networks, cognition and culture. Approaches and findings are explored in a series of methodological tutorials, examples and case studies in which the hypotheses and theoretical frameworks are supported.

1968 Douglas R. White. Download: Societal Research Archives System: Retrieval, quality control and analysis of comparative data. In R. Naroul and R. Cohen, eds. Handbook of Method in Cultural Anthropology, pp. 676-685. Preprinted at Social Science Information 7(3): 78-94 (poor image)

Abstract. The Societal Research Archives System (SRAS) was created by the author in 1966 as a computer-based retrieval and research facility for comparative data in social science. The basic idea was to integrate all of the available cross-societal coded data from published and unpublished sources into a single data base, and secondly to develop computer programs which would facilitate all of the steps in comparative research, from sample selection and data retrieval to correlation, data quality control, and testing for genetic, diffusional, or functional sources of correlation. This paper will serve to explain the present operation of the system. Additional work is being done at the University of Pittsburgh's Cross-Cultural Cumulative Coding Center, beginning in 1968, on the refinement and expansion of the system, which will be the subject of a future report. (see: Standard Cross-Cultural Sample)




1974 Douglas R. White. Download: Mathematical Anthropology. J.J. Honigmann, Ed., Handbook of Social and Cultural Anthropology: pp. 369-446 New York: Rand-McNally. Erratta

Abstract. This review introduces the general reader to some of the uses of mathematics in the analysis of ethnographic data in order to intensivy the conceptual and explanatory power of anthropological theory. Many of the problems currently modeled by mathematics are of such general relevance to anthropological theory that is is doubtful that they should be confined under the title of mathematical anthropology. What unites them under this rubric is not quantification, which covers a fraction of mathematics, but rather the common logical substructure that mathematics shares with science in the use of axiomatic reasoning. The major thrust here is to show advances in refining the logical underpinnings of mathematical systems of analysis in anthropology in recend decades.
The rubrics examined are (1) processual analysis (probabilistic and deterministic models), (2) optimization analysis (decision rules, linear programming, game theory, flows in networks, dynamical models), (3) structural analysis (graph theory, signed graphs, and balance theory for social networks), and (4) ethnographic decomposition (natural information processing systems, ordering and transformational rules, decision rules, grammatical rules in cultural systems, abstract algebraic decomposition, relative product algebras for kinship terms and networks, blockmodeling, and crtitique of componential analysis).



1985 Michael L. Burton, Douglas R. White. Download: Division of Labour by Sex. Eds. Adam Kuper, Jessica Kuper, Encyclopedia of the Social Sciences: pp. 206-207 London: Routledge. Reprinted 2004, pp. 239-240.

Abstract. The sexual division of labour is a basic structural element in human social organization. Humans are the only primates who have a highly developed sexual division of labour in food production. They also are the only primates that share food on a regular basis. However, there is substantial variability in the sexual division of labour across societies and the female contribution to food supply in foraging societies is far greater than was once believed. Evidence for the original human division of labour comes from two sources: primate ethology and the ethnology of foragers. Male specialization in hunting is consistent with the tendency of male terrestrial primates to specialize in defense, a specialization that gives a selective advantage to larger males. Sexual dimorphism is a consequence of this original division of labour. However, while it is true that in forager societies, men lend to hunt and women to gather, early studies of foragers greatly underestimated the importance of female gathering. They therefore exaggerated the dependence of wives on their husbands. Modern studies of foragers (Lee and DeVore 1968) show that women's gathering often contributes more than half of the subsistence calories, The rise of cross-cultural and cross-national research makes it possible to estimate the relative frequencies of male and female effort to various tasks. As a result of Murdock's work (Murdock 1937; Murdock and Provost 1973) we now have cross-cultural codes on sexual division of labour for fifty tasks. These codes confirm earlier generalizations about near-universals. Tasks done by males in more than 95 per cent of the sample societies include hunting large land animals, metal-working, wood- and bone-working, boat building, and trapping. Tasks done by females in more than 95 per cent of the sample include only cooking and care of infants.
Patterns of sexual division of labour appear to have only a partial basis in biology, and most tasks exhibit high variability. This is especially true of the important food-production tasks pertaining to agriculture and the care of domesticated animals. These variations, however, fall within constraints of a relative rather than universal nature. Many researchers have sought rules of consistency in the variable allocation of tasks. While earlier researchers emphasized the male strength advantage, research in the 1970s placed more emphasis on constraints due to the reproductive specialization of women. Brown (1970) emphasized the compatibility of women's tasks with simultaneous childcare responsibilities. Women's tasks are likely to be relatively close to home, not dangerous, and interruptible.
Burton, Brudner, and White (1977) proposed that these relative constraints produce entailments within production sequences. E.g., Women tend to take on additional tasks within production sequences in an order that begins with tasks closer to the home and ends with tasks farther afield. Men take on additional tasks in the opposite order from the more distant to those closer to home. Burton and colleagues found entailment chains for the following production sequences: animal tending, animal products, textiles, fishing and agriculture. An example from agriculture: if women clear the land, they also prepare the soil: if the latter, they also plant, tend crops, and harvest. If they tend crops, they also fetch water, and if they plant, they also prepare vegetables for cooking.



2003 Douglas R. White. Download: Ties, Weak and Strong. Encyclopedia of Community Vol. 4:1376-1379. Edited by Karen Christensen and David Levinson. Thousand Oaks, CA: Sage Reference.

Abstract. This entry reviews the relationships among the biased networks models of Rapoport, the small-world problem posed by Milgram and later addressed by Watts, and studies of community cohesion in relation to the strength of weak ties hypothesis of Granovetter








2008 Douglas R. White, Download: Standard Cross-Cultural Sample, International Encyclopedia of the Social Sciences, 2nd edition, Ed., William A. Darity, Jr. Vol. 8. pp. 88-93. New York: Macmillan Reference USA Draft 1.1

Abstract. The Standard Cross-Cultural Sample, or SCCS (Murdock and White 1969), is a cumulative and collaborative database of coded variables on maximally diverse and ethnographically best-described societies used by scholars in the social sciences. The champion of modern cross-cultural and statistical methods, George P. Murdock, in preparation for a standard sample, had classified the 1,267 societies in his coded Ethnographic Atlas into 200 distinctive world cultural provinces (Murdock 1962-1967, 1968). Douglas R. White (1968) had compiled a database of coded cross-cultural studies and done a concordance of previous samples (repeated by Ember 1992) that showed the fruitlessness of testing hypotheses that involved vari- ables from different studies because there was little over- lap between randomly drawn or ad hoc samples. White (1969), linked to the Columbia-Michigan historical-evo- lutionary successor to the Boasian school, had just completed the first comparative historical study to use Murdock's Ethnographic Atlas codes in a regional study. The dual-authored approach to the SCCS signified a rapprochement between the Yale school of evolutionary functionalism and the historical anthropological schools at Columbia, Michigan, and Berkeley. Their founding of the Cumulative Cross-Cultural Coding Center (CCCCC) for the SCCS at the University of Pittsburgh (1968-1973), like their 1969 authorship, was coequal, although they were born nearly fifty years apart.


Since 1969, hundreds of cross-cultural studies have contributed coded data using the Standard Cross-Cultural Sample. Some of uses of the SCCS are describing and findings illustrated by reviewing the ideas in major books whose authors coded new data as well as evaluating theories tested from the new and cumulative database.

See also the Wikipedia sites, 2006: Standard Cross-Cultural Sample and Galton's problem



2009 Douglas R. White. Download: Dynamics of Human Behavior (Cohesion and Resistance). Encyclopedia of Complexity and Systems Science. Berlin, Heidelberg: Springer-Verlag. (IMBS preprint). Santa Fe Institute working paper

Abstract. I review network aspects of human dynamics that link macro-historical to micro-sociological and evolutionary processes. The ability to bond in communities of varying spatial scales is a special property of humans that happens through social networks. These networks have greater cohesion through invulnerability to disconnection without removal of k nodes. Menger's (1927) connectivity theorem shows that this property of k-cohesion mutually entails k node-independent paths between every pair of group members. Because of this property, i.e., by redundancy of communication, humans in such communities can utilize language and long-range communication to compensate for diminishing face-to-face interaction as groups grow large. For a given level k of cohesion, the maximally extensive e(k) group size is unbounded and scalable because, for each cohesive intensity level k, the maximal group size e(k) can expand indefinitely without the need to increase the average number of ties per member. Hence, the growth of human community size is scalable at a fixed cost in number of ties per person, unlike those species unable to take advantage of k-connectivity. Strong causal effects, using the k cohesion-level measure of empirical groups whose boundaries and extent are defined by e(k), have been replicated and validated in various sociological and anthropological network studies. This allows me to explore here the micro-macro linkages, the social and historical dynamics of socially cohesive networks, between scalable properties of k-cohesive groups and concomitant sociopolitical processes. Qualitative dynamics of major historical processes in human behavior, which are related for example to warfare and empire formation, are consistent with scale-up of sociopolitically k-cohesive groups. Such groups expand across metaethnic frontiers to evoke resistance that operates through scale-up of k-cohesive growth-by-opposition. Some current studies of such issues (Turchin 2003, 2005) use sufficient levels of aggregation to successfully assess dynamic interactions between macro-variables in sociopolitical processes (some of which involve political unit cohesion and scale). Others, such as the conflict studies of Lim, et al. (2007), use field-theory models of spatial interaction. New hypotheses, questions, and results may help link scalable k-cohesive groups to human evolutionary modeling and to variables used in evolutionary models of cooperativity and of transitions in sociopolitical organization. These various kinds of empirical studies illustrate concepts and methods in dynamics and complex systems applicable to human behavior in the domains I review. The mainline arguments illustrated here are expanded by reviews of work on other causal process models that combine micro-analysis of sociopolitical and economic behavior in the context of institutions, networks, historical ethnography, and network economic experiments. I note new directions flourishing in causal modeling, including multifractality and agent behavior, that evince further need for development of historically longitudinal databases, advancement of methods for dynamical analyses, and use of multilevel modeling that incorporates network representation and conceptualization.

Abstracts and links to published articles and chapters in PDF format and 15 unpublished papers



2012 Douglas R. White. Download: Networks and Globalization Policies. Chapter 9, in, Balàzs Vedres, and Marco Scotti (editors), Networks in Social Policy Problems. Cambridge UK: Cambridge University Press. (not yet a Santa Fe Institute working paper)

Abstract. The need for a new economy is deeply rooted in Western history. The assertions of this chapter, summarized here, will make that evident. These deeper historical perspectives are needed to understand today's conundrums. In the early Medieval Renaissance, center and periphery were based on betweenness centrality (on shortests paths), which, within Europe, gave advantages to local hubs such as Genoa. In these kinds of trading systems, commercial ethics dominated, with emphasis on building trust in order to expand markets. But as betweenness centrality for Europe began to yield advantage to cities on its eastern boundary, and with pan-Eurasian trade routes opened by the Golden Horde under a commercial ethic "or else," i.e., conquest, Europeans from 1300 on began attempts to penetrate the more distant control points for pan-Eurasian trade. Center and periphery began to take a new shape, that of flow centrality (sum of flow capacities), which has no bounds in trading systems, so the competition is all against all, in a single-winner model. Thus, as early as 1450, European naval powers such as Portugal initiated policies of conquest for purposes of forced trade at forced prices. The guardian ethic of what's ours is not to be shared, what's ours is to be protected, pushed aside the commercial ethic that had flourished earlier in East Asia. Portugal conquered the far Eastern port cities to establish protection rackets. Following the conquest of the New World by Europeans, north European cities took over the positions of financial flow betweenness. Global outreach developed power centers shifting to the Dutch, the English, the British Industrial Complex, and eventually the U.S., without a break in military-based economic policies of trade, which by definition is coerced exchange lacking fair pricing. The English "Glorious Revolution" of 1698, resulting in a peaceful integration between Protestant and Catholic citizens and contenders for the Crown, came about with the anomaly of truly commercial trade by (British) East India Company sea captains, who recurrently defected from their EIC corporation in their second year to trade on their own account in South Asia. This malfeasance towards the EIC through private trade became so intense, it has been argued, that it created the first fully free market ungoverned by states and military policies, thus creating the "market economy." The EIC formally abandoned intraregional trading, which by 1680 was left to individuals. Once the company withdrew, however, the return of sea captains and traders to London created a entrepreneurial and merchant-empowered legislature that disempowered the landowning elites and created what was effectively the first modern commercially-based democracy. Private trade to the East continued to 1824 and beyond, with many additional predations of Europe on India and China. Unfortunately the policy of European governments, following the notion advanced by Modelski of evolution of the World System through "evolutionary learning," even while modernizing, continued the practice of militarily dominated trade. Under these circumstances, the potential for what would otherwise be "free markets" was not realized in terms of having fair pricing or fair remuneration to labor, or consideration of the ecological costs and damages of militarily dominated trade. In the broader historical sweep, it can be concluded that militarily dominated trade, continued in the present era, and the Guardian ethic of "what's ours is ours, not to be shared, and defended at all costs for us alone" continues to be implicated today in the financial meltdowns of 2008-into the future. The policy remedy is a return to the commercial ethic of fairness, trust established by regulations and punishment for illegal actions, and cooperativity. Fairness is established, from families to Champaigne fairs, by repeated evidence of consistency in behavior. Portuguese militaristic trade was an example of the diametric opposite: threaten to destroy others unless they give the price wanted, use overwhelming force on those who don't agree, charge protection money from those who accede, and never relent on prices. Walmart is a modern variant, using techniques used in the military procurement overseas, which implants an extra dimension of demanding prima facie unfair procurement prices. We need a new economic perspective and fairness systems design. This article contains the evidentiary construction drawing from historical sources and analyses intended to validate these assertions and my conclusions.

2009 Frank Schweitzer, A. Vespignani, Giorgio Fagiolo, Didier Sornette, Fernando Vega-Redondo and Douglas R. White. Download: Economic Networks: The new challenges. Science 325, 422-424.

2009 Frank Schweitzer, Giorgio Fagiolo, Didier Sornette, Fernando Vega-Redondo and Douglas R. White. Download: Economic Networks: What Do We Know and What Do We Need To Know? Advances in Complex Systems 12(4-5):407-422. Santa Fe Institute working paper

2006 Douglas R. White, Natasa Kejzar, Constantino Tsallis, Doyne Farmer, and Scott White. Download: A Generative Model for Feedback Networks (including trade, biotech, kinship) Physical Review E 73, 016119 (8 pages) abstract (http://tinyurl.com/ylpbn3) doi:10.1103/PhysRevE.73.016119
http://arxiv.org/abs/cond-mat/0508028
reviewed 2005 in Europhysicsnews 36(6):218-220 by Stefan Thurner:
Santa Fe Institute Working Paper 2005

Reprinted: Virtual Journal of Biological Physics Research February 1, 2006 issue. The Virtual Journal, which is published by the American Physical Society and the American Institute of Physics in cooperation with numerous other societies and publishers, is an edited compilation of links to articles from participating publishers, covering a focused area of frontier research. The implications of this type of model are carried further in Thurner, Kyriakopoulos and Tsallis, 2007, Unified Model for Network Dynamics Exhibiting Nonextensive Statistics Phys. Rev. E 76, 036111 (2007) (8 pages).

paj file 1250-0-2-0 | R code | Edge Based Model simulation for alpha = 0 (start), beta=1.9 (distance decay), gamma = 0 (route), N=500, steps of 15 shown in figures with black lines as tree-like links to new nodes, red lines are feedback links at various (clickable) distances. See Working Papers Series for the Social Dynamics and Evolution group for full color preprint as well as an interactive conference PDF by Kejzar.

Abstract. We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element of network growth. The underlying graphs in these situations grow via a competition between cycle formation and node addition. After choosing a given node, a search is made for another node at a suitable distance. If such a node is found, a link is added connecting this to the original node, and increasing the number of cycles in the graph; if such a node cannot be found, a new node is added, which is linked to the original node. We simulate this algorithm and find that we cannot reject the hypothesis that the empirical degree distribution is a q-exponential function, which has been used to model long-range processes in nonequilibrium statistical mechanics.

Wikipedia: Social-circles network model

For comparison with empirical distributions see the Retrofitting site

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2007 Role Models for Complex Networks: Joerg Reichardt and Douglas R. White. The European Physical Journal B 60, 217-224 and selected as a 2008 'Highlight' paper of Europhysics News 39(1):11 . Preprint at arXiv:0708.0958v1: 1-14 Subjects: Physics and Society (physics.soc-ph); Data Analysis, Statistics and Probability (physics.data-an) Cite as: arXiv:0708.0958v1 [physics.soc-ph]. link to the world economy blockmodel paper with Joerg Reichardt via a review by Cosma Shalizi Santa Fe Institute Working Paper 07-12-045

Abstract. We present a framework for automatically decomposing ("block-modeling") the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph ("block model") depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy.

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Movie Visualizations: The Evolution of Inter-Organizational Collaboration In the Life Sciences

2005 Walter W. Powell, Douglas R. White, Kenneth W. Koput and Jason Owen-Smith. Network Dynamics and Field Evolution: The Growth of Interorganizational Collaboration in the Life Sciences. American Journal of Sociology 110(4):1132-1205 (has full text in pdf as well as html with enhancements) electronic edition
Available at a library near you Download: SFI-WP2003d.pdf See link to movies at Barabasi site Santa Fe Institute Working Paper

This paper received the 2007 Viviana Zelizer Distinguished Scholarship Award given every two years by the American Sociological Association's Economic Sociology Section. The award recognizes an outstanding article published in the field of economic sociology in the previous two years. The award letter states that the paper "advances several questions central to economic sociology," and the award committee letter of congratulations states: "We see this piece as groundbreaking; we expect it will continue to be highly useful and frequently cited over the long run in our subfield." .

Abstract: We develop and test, using McFadden's discrete choice statistical modeling applied to network dynamics, four alternative logics of attachment - - accumulative advantage, homophily, follow-the-trend, and multiconnectivity - - to account for the development of interorganizational collaboration in the field of biotechnology. The commercial field of the life sciences is characterized by wide dispersion in the sources of basic knowledge and rapid development of the underlying science, fostering collaboration among a broad range of institutionally diverse actors. We map the network dynamics of the field over the period 1988-99. Using multiple novel methods, including analysis of network degree distributions, network visualizations, and multi-probability models to estimate dyadic attachments, we demonstrate how a preference for diversity shapes network evolution. Collaborative strategies pursued by early commercial entrants are supplanted by strategies influenced more by universities, research institutes, venture capital, and small firms. As organizations increase both the number of activities around which they collaborate and the diversity of organizations with which they are linked, cohesive subnetworks form that are characterized by multiple, independent pathways. These structural components, in turn, condition the choices and opportunities available to members of a field, thereby reinforcing an attachment logic based on connection to partners that are diversely and differently linked. The dual analysis of network and institutional evolution offers a compelling explanation for the decentralized structure of this science-based field.

2004 Douglas R. White, Jason Owen-Smith, James Moody, and Walter W. Powell Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings. Computational and Mathematical Organization Theory 10(1):95-117. Santa Fe Institute Working Paper Special issue on Mathematical Representations and Models for the Analysis of Social Networks within and between Organizations, Guest Editors Alessandro Lomi and Phillipa Pattison. Download:
CMOT site

Abstract: Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.

Keywords: Graph theory, social networks, algorithmic detection, cohesive network topologies, fields, organizations, micro-macro linkages.

2003 James Moody and Douglas R. White, Structural Cohesion and Embeddedness: A Hierarchical Concept of Social Groups. American Sociological Review 68(1):103-127. Santa Fe Institute Working Paper Implemented in NetMiner v2.4.0 (fall 2003). - ASA posting of the article pdf on the Association web-page:

This year's Outstanding Article Award of the year 2004 by the ASA Mathematical Sociology Section goes to James Moody and Douglas White for their article "Structural Cohesion and Embeddedness: A Hierarchical Concept of Social Groups" which appeared in the American Sociological Review, February 2003. This paper develops a new graph-theoretic treatment of structural cohesion based on node connectivity, capturing the intuition that more cohesive groups should be better able to survive the loss of group members. Their method detects group structure, identifying both overlapping and hierarchically nested subgroups at different levels of cohesion, and also generates a measure of each actor's embeddedness within the group. Their empirical analyses of high-school friendship networks and corporate interlocking directorates reveal the explanatory power of structural cohesion controlling for other commonly used network measures such as degree and centrality. By offering a more precise conceptualization of the key sociological concepts of "solidarity" and "embeddedness," Moody and White have demonstrated the value of mathematical sociology, and we are pleased to present them with this award.

Abstract: While questions about social cohesion lie at the core of our discipline, no clear definition of cohesion exists. A definition of social cohesion that leads to an operationalization of social embeddedness based on network connectivity measures cohesiveness as the minimum number k of actors whose absence would disconnect a group. Two members of a group with cohesion level k automatically have at least k different ways of being connected through independent paths. This definition generates hierarchically nested groups, where highly cohesive groups are embedded within less cohesive groups. We discuss the theoretical implications of this definition and demonstrate the empirical applicability of our conception of nestedness by testing the predicted correlates of our cohesion measure within high school friendship and interlocking directorate networks. The positive results of these tests reinforce those of other studies in what we have come to call Predictive Cohesion Theory.

Keywords: Graph theory, social networks, algorithmic detection, cohesive groups, social boundaries

2009 Chapter 5: Innovation in the Context of Networks, Hierarchies, And Cohesion. David Lane, Denise Pumain, Sander van der Leeuw, and Geoff West, eds. Complexity Perspectives in Innovation and Social Change. Dordrecht: Springer Methodos Series.

Abstract.

The ability to specify models of social processes in relatively precise terms proves to be central to historical dynamics and to a macro-approach to innovation and social change as well as to micro-approaches.

This chapter views innovation and social change as occurring in social networks. It is less concerned with how, or precisely what innovations occur than with when and where they occur, and, in terms of context, why.

The focus on network approaches emphasizes the specification of a series of consequential concepts associated with the notions of 'cohesion' and 'hierarchy' in mathematics, the physical sciences, and the social sciences.

A specification of the first of these concepts, structural cohesion, provides a basis for measuring the specific strength and nature of bonds and linkages that help to define and evaluate important group-level processes in historical and social dynamics. The second concept, that of hierarchy, is important to determine aspects of agency, but requires working through multiple sources of network measurement (multiple relations, multiple kinds of nodes and agents) in order to specify and test processual theories of social and historical dynamics linked to innovation and social change.

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2009. Getting Connected: Networks of kinship and compadrazgo in rural Tlaxcala, Mexico". Michael Schnegg and Douglas R. White. Pp. 37-52, in Networks, Resources and Economic Action: Ethnographic Case Studies in Honor of Hartmut Lang (Kulturanalysen), Eds., Clements Greiner and Waltraud Kokot. Berlin: Dietrich Reimer Verlag.

2008 A Normalized and a Hybrid Modularity Haifeng Du, Douglas R. White, Yike Ren, Shuzhuo Li. Sumitted to Physical Review E.

Abstract. The study of community structures is a hot spot for many inhomogeneous networks. Modularity plays an important role in this area, because it is a criterion for community detection, and a basis for community detection algorithms. Although commonly used in papers concerning community structures, modularity is seldom fully studied. In this paper, we investigate problems with the properties of modularity as defined by Newman and we propose a modularity normalized for number of groups as well as a hybrid modularity that improves on properties that reflect the interactions among communities. We also illustrate the basic flowchart of a "bottom-up merging" community detection strategy based on the properties of modularity, and explore a detection algorithm inspired by hybrid modularity.

2001 Fast Approximation Algorithms for Finding Node-Independent Paths in Networks Douglas R. White and MEJ Newman. Santa Fe Institute Working Paper 01-07-035.

Abstract. A network is robust to the extent that it is not vulnerable to disconnection by removal of nodes. The minimum number of nodes that need be removed to disconnect a pair of other nodes is called the connectivity of the pair. It can be proved that the connectivity is also equal to the number of node-independent paths between nodes, and hence we can quantify network robustness by calculating numbers of node-independent paths. Unfortunately, computing such numbers is known to be an NP-hard problem, taking exponentially long to run to completion. In this paper, we present an approximation algorithm which gives good lower bounds on numbers of node-independent paths between any pair of nodes on a directed or undirected graph in worst-case time which is linear in the graph size. A variant of the same algorithm can also calculate all the $k$-components of a graph in the same approximation. Our algorithm is found empirically to work with better than 99% accuracy on random graphs and for several real-world networks is 100% accurate. As a demonstration of the algorithm, we apply it to two large graphs for which the traditional NP-hard algorithm is entirely intractable--a network of collaborations between scientists and a network of business ties between biotechnology firms.

2007 Oscillatory dynamics of city-size distributions in world historical systems (draft). Douglas R. White, Laurent Tambayong, and Natasa Kejzar. Globalization as Evolutionary Process: Modeling Global Change. G. Modelski, T. Devezas and W. Thompson, eds. Pp. 190-225. London: Routledge. MBS Working Paper 07-04

Abstract. Oscillatory patterns of expansion/contraction have long characterized the dynamics of demographic, economic, and political processes of human societies, including those of exchange economies and globalization. Major perturbations in city-size distributions are shown to exist for major regions in Eurasia in the last millennium and to exhibit some of the characteristics of cyclical oscillations on the scale of 100s of years as well as longer fluctuations, from 400 up to 800 years, between periods of major collapse, often punctuated by lesser collapse. Variations in timing, irregularities in amplitudes, and ups and downs in our measures appear to correlate with some of the peaks and troughs in urban population growth and show long-cycle correlations with J.S. Lee's (1931) sociopolitical instability (SPI) data on the durations of internecine wars for China. We focus here on central civilization within the world cities database, including China and Europe, and the Mid-Asian region between. These data are likely to reflect changes in the macro regions connected by trade networks, where we would expect synchronization. Our interpretation of city-size distribution oscillations is that they follow, with generational time lags, rises and falls in the expansion/contraction of multi-connected trade network macro zones, with Zipfian city-size hierarchies tending to rise with trade network expansions and fall with contractions. City system rise and fall also tend to couple with oscillations of population relative to resources interacting with SPI in total cycles that average about 220 years. Time-lagged synchronies in the dating of phases for city distributions in different regions that are connected by multiple routes of trade, as noted tentatively by Chase-Dunn and Manning (2002:21), at least in the rising and more Zipfian phase, support the existence of city-system rise and fall cycling. We find evidence that rise and fall in Silk Road connectivities between China and Europe had time lagged effects on the growth of power law tails in European urban hierarchies; that changes in Mid-Asia city distributions led weakly those in China while those in China led strongly those in Europe, at different time lags. Maximal likelihood of two different measures of city size distributions proved to be of central importance to this paper, as they provide unbiased estimates of statistical parameters and improve confidence limits significantly, the more so for those smaller sample sizes in city data available in many historical periods. Analyses of these estimates supports six major sets of hypotheses about urban system evolution and fail to contradict two more speculative hypotheses about evolutionary learning in global systems.

---

2007 Network Structures in Industrial Pricing: The Effect of Emergent Roles in Tokyo Supplier-Chain Hierarchies Tsutomu Nakano and Douglas R. White. Structure and Dynamics 2(3): 62-110.

Abstract. Given data on supplier chains in a Tokyo industrial district, we show how network structures such as monopsony (uniqueness of buyers) may affect noncompetitive pricing. To address the distribution of these biases we show how two types of emergent roles in hierarchically organized production chains affect noncompetitive price diffusion both horizontally and vertically in the industrial hierarchy. More concretely our model addresses such questions as how it is that, as in the case of this specific industrial hierarchy, processing activities and parts and components manufacturing organized by the 'elite' buyers for the top manufacturers, while executed by numerous smaller enterprises lower in Ohta hierarchy, leave so many low-level suppliers subject to monopsony. Monopsony and monopoly (and to a lesser extent, duopoly and duopsony) are structures that may severely reduce profit margins. We use two complementary frameworks to pose and address such questions. One is network economics where monopsony and duopsony and their potential effects on pricing are well defined, like those of monopoly and duopoly. The other is network sociology, where we can define more fundamental concepts of the network construction of social and economic processes and institutions and the effects of network structure in transactional situations. We regard both frameworks as necessary to modeling elements of global and regional economies.

2006 The Large-Scale Network of a Tokyo Industrial District: Small-World, Scale-Free, or Depth Hierarchy? Tsutomu Nakano and Douglas R. White. Working paper June 2006, Center on Organizational Innovation Working Papers. ISERP, Columbia University.

Abstract. The large-scale networks of suppliers and buyers in industrial districts have rarely if ever been studied as social networks due to analytical complexity and rarity of datasets. We quantitatively analyzed such a complex system to identify its mechanisms of integration. Tests of the small-world model failed because of a power-law degree distribution, shorter-than-random average distances, and lack of local clustering. The scale-free network model was also rejected because primarily hubs organized the network not preferences of suppliers. A directed acyclic graph (DAG) model explained the structural properties. Finally, in lieu of small-world or scale-free models, we offer statistical evidence that the DAG should be a general property for the complex production networks, as modeled by Harrison White.

2006 Power-Law and "Elite Club" in a Complex Supplier-Buyer Network: Flexible Specialization or Dual Economy? Tsutomu Nakano and Douglas R. White. Working paper May 2006, Center on Organizational Innovation Working Papers. ISERP, Columbia University.

Abstract. After the 1990s, original equipment manufacturers (OEM) as multinational conglomerates have become more powerful than ever, exerting control over their suppliers, owing in part to the advanced machining and information technologies. Is this a revival of the traditional Marxian framework, or a "dual economy"? Conducting network analysis of supplier-prime buyer relations among over 8,300 firms in an industrial district, we found not only structural properties of "flexible specialization" as a division of labor among dedicated small- and medium-sized suppliers but also an invisible "elite club" or cohesive core composed of extremely powerful OEMs plus their elite suppliers, employing analyses of cohesion and assortative correlation in the structural embedding. An overwhelming majority of the suppliers were not free from dependency upon the core in order to gain access to and social endorsement from the consumers, as substantiated by the overall power-law node links, against the claims of "flexible specialization." The present study suggests a "dual economy" not on the basis of firm size as traditionally claimed, but of competition to be suppliers of prominent OEMs in the acyclically hierarchical network, from the relational approach of network integration mechanisms, as a latent but decisive explanatory variable.

2006 The Visible Hand in a Production-Chain Market: A Market Equilibrium from Network Analytical Perspective Tsutomu Nakano and Douglas R. White. Santa Fe Institute Working paper 2006,

Abstract. We analyze general price equilibrium mechanisms of production-chain markets, comparing the producer market model proposed by Harrison White with hypothesized network effects on pricing that emerge from empirical analysis of trade relationships among over 8,000 firms in a large-scale industrial district in Tokyo. Consistent with White’s model, the supplier-prime buyer relationships are strictly hierarchical and constitute a directed acyclic graph (DAG). There are no exchange cycles that would promote price equilibrium. We argue, partly from a Simmelian approach to triad configurations, that three linked network configurations are likely to affect pricing. First, a particular form of structural cohesion as defined by multi-connectivity (bicomplete connectedness within a large bicomponent) is a critical “seeding” mechanism where quasi-optimal exchange can be achieved as the “visible hand” in production-chain markets. Second, a powerful core of elite firms was detected that organizes status differences among firms and serves to institutionalize role structures in the production markets. Third, structural advantages in pricing accrue to elite core firms because suppliers upstream in the hierarchy operate through a 4:1 preponderance of multiple-supplier to multiple-buyer triads, which enforces competition among themselves rather than among the buyers. These pricing benefits to buyers are passed along to the downstream elite firms. The elites can exert power over the complex network through the serial divisions of labor embedded in the tiers of subcontracting hierarchies, dominating price-setting from the top.

1999 "Controlled Simulation of Marriage Systems." Journal of Artificial Societies and Social Simulation. http://jasss.soc.surrey.ac.uk/2/3/5.html

Abstract. This article presents and illustrates a new methodology for testing hypotheses about the departure of marriage choices from baseline models of random mating in an actual kinship and marriage network of a human population. The fact that demographic constraints can drastically affect the raw frequencies of different types of marriage suggests that we must reexamine or even throw out - as methodologically flawed - statistical conclusions regarding marriage "rules" from most of the existing empirical case studies. The development of the present methods, in contrast, enables researchers to decompose those behavioral tendencies that can be taken as agent-based social preferences, institutional "rules" or marriage structure from those behaviors whose divergent frequencies are merely a by-product or epiphenomena of demographic constraints on the availability of potential spouses. The family of random baseline models used here enables a researcher to identify overall global structures of marriage rules such as dual organization as well as more local of egocentric rules such as rules favoring marriage with certain kinds of relatives. Based on random permutations of the actual data in a manner that controls for the effects of demographic factors across different cases, the new methods are illustrated for three case studies: a village in Sri Lanka with a novel form of dual organization detected by this methodology, a cross-class analysis of a village in Indonesia, and an analysis of a farming village in Austria in which a structurally endogamous subset of villages is identified by the method and shown to form the backbone of a class-based landed property system.

1998 "Taking Sides: Marriage Networks and Dravidian Kinship in Lowland South America" (M. Houseman & drw) in Transformations of Kinship. pp. 214-243, in eds. Maurice Godelier, Thomas Trautmann and F.Tjon Sie Fat. Washington, DC: Smithsonian Institution Press.

Abstract. Dual organization is a unifying concept underlying seemingly dissimilar alliance structures. We explore this idea with reference to lowland South America where dual organization is common. We have chosen, however, to place primary emphasis on the patterning of actual marriage networks. Our aim is to identify the invariant properties of such networks and, in the light of these findings, to reconsider the relationship between marriage network structure and other, categorical or jural features of social organization: kinship terminologies, descent principles, marriage rules, etc. As a means to this end, we develop the concept of matrimonial "sidedness". In doing so, we derive new results concerning dual organization and a new understanding of dravidianate systems.

This analysis is based, on the one hand, on published genealogical data concerning the Makuna (Arhem 1981), the Pakaa-Nova (Vilaca 1992), the Yanomamo (Chagnon 1974), the Trio (Riviere 1969), the Parakana (Fausto 1990), the Waimiri-Artroari (Ferreira da Silva 1993), the Guahibo (Metzger 1968), the Shavante (Maybury-Lewis 1967) and the Suya (Seeger 1981), and on the other hand, on Hornborg's (1988) comparative study of 48 lowland South American societies.

2002 "Conectividad Multiple, Fronteras e Integracion: Parentesco y Compadrazgo en Tlaxcala Rural" Douglas R. White, Michael Schnegg, Lilyan A. Brudner, and Hugo G. Nutini, Capitulo 4, Analisis de Redes 41-94. Eds. Jorge Gil Mendieta y Samuel Schmidt.

Abstract. This chapters deals with the social integration and its boundaries. How is a particular locality integrated? How are social frontiers constructed in a region? How is locality inccribed within the larger economic and sociopolitical spheres?

1977 "Community Variations and Network Structure in the Social Functions of Compadrazgo in Rural Tlaxcala, Mexico" Nutini, Hugo G., and Douglas R. White. in Ethnology 16:353-384.

Abstract. None.
2005 Contents and Introduction - Network Analysis and Ethnographic Problems: Process Models of a Turkish Nomad Clan. Douglas R. White and Ulla C. Johansen. Boston: Lexington Press. ISBN # 0-7391-0896-4. review copy available

Abstract. The introductory chapter introduces and illustrates four propositions about network theory and emergence:

• Networks have structural properties (local and global) that have important feedback on behavior and cognition. This section reviews the probabilistic and scaling theories of network topology and dynamics, evidence for feedback process in networks, many of which are "out of range" for perception even by the best of ethnographers. Adamic, Lukose and Huberman's (2003) findings are reviewed insofar as network scaling properties alter the ratio between local inequality (heterarchy that allows network navigation) and global inequality or network hierarchy, i.e., this ratio changes as a function of self-similar or scale-free properties of network topologies. All the current interdisciplinary work on network scaling is reviewed in this light in relation to social processes, problems of observation, and the understanding of social dynamics.
• Micro-macro (and macro-micro) linkages offer explanatory principles, some of which are highly deterministic. Mathematical theorems concerning structural and probabilistic relations between micro and macro properties of networks are reviewed to show how theoretical explanations about social structure and organizational dynamics can be formulated in terms of general scientific principles. Balance, clustering, relational equivalence, structural cohesion, and network embedding are examined as explanatory models that allow the formation of models and explanations that are consistent with general theoretical principles.
• Many structural properties have configurational effects, whether or not they have micro-macro linkages. Here, the effects of structure per se are examined, as consequences of proximal effects of principles such as reciprocity and network embedding.
• Emergents may be local or nonlocal, depending on whether they have micro-macro linkages. Clarifications of the continuum of structural effects from local to nonlocal are shown to relate to needed clarification of a concomitant continuum for the varying meanings of emergence.

  The argument is developed that analysis of network structure and dynamics is not only valid but necessary for any ethnographic, historical, or longitudinal approach to understanding social processes. Network analysis offers a fully generalizable and multilevel (including heterarchic) approach both to coding events and relations occurring among multilevel actors and their environments, and to theorizing social interplay between structure and dynamics. Rule-based regularities are distinguished from emergent structural properties that have configurational effects. Models and emergent phenomena are distinguished by how such properties interact with the presence or absence of micro-macro linkages.

  Five propositions are advanced for "when does network analysis matter?" and the problems of expected and unexpected change arising out of network and multiagent interactions. Given our findings about the limits of ethnographer knowledge regarding organizations, groups and the formation of knowledge communities, we show how network analysis can provide crucial components of an understanding of emergent rules and emergent groups. We focus especially on the explanatory power and context of hierarchically and heterarchically embedded layers of structurally cohesive groups in social networks and the vistas, measurements and general explanatory principles that these can provide to ethnography in particular and understanding social dynamics in general. The introductory chapter is intended to provide a new theoretical context for a coherent and encompassing network approach to ethnography and social theory that is capable of driving whole new classes of results from the analysis of the rich data provided by ethnographers and ranging from observed relationships to the full richness of the symbolic media of interpersonal and culturally mediated interactions.

  See the reviews for reader reactions and related articles in Chronicling Cultures and the journal Complexity. The glossary of the book provides the reader with conceptual and technical background in the fields of complexity theory, networks and graph theory, social and kinship organization, and general ethnographic and sociological vocabulary.

  2005 Douglas R. White. Ring Cohesion Theory in Marriage and Social Networks Social Networks special issue edited by Alain Degenne Mathematiques et sciences humaines 168:5-28 Journal of the Ecole des Hautes Etudes en Science Sociales, Paris Download: RingCohesionMarriage.pdf Tools for Marriage Network Analysis

  Structural studies are, in the social sciences, the indirect outcome of modern developments in mathematics which have given increasing importance to the qualitative point of view in contradistinction to the quantitative point of view of traditional mathematics. It has become possible, therefore, in fields such as mathematical logic, set theory, group theory, and topology, to develop a rigorous approach to problems which do not admit of a metrical solution. The outstanding achievements in this connection - which offer themselves as springboards not yet utilized by social scientist - is to be found in J. von Neumann and O. Morgenstern, Theory of Games and Economic Behaviour; N. Wiener, Cybernetics; and C. Shannon and W. Weaver, The Mathematical Theory of Communication. (Lévi-Strauss 1968, Chapter XV, Social Structure, section on "Structure and Measure")

  2005 Klaus Hamberger, Michael Houseman, Isabelle Daillant, Douglas R. White and Laurent Barry. Matrimonial ring structures Social Networks special issue edited by Alain Degenne Mathematiques et sciences humaines 168:83-121. Journal of the Ecole des Hautes Etudes en Science Sociales, Paris Download: MatrimonialRingStructure.pdf Tools for Marriage Network Analysis
  Figures from article

  SUMMARY: The paper deals with matrimonial rings, a particular kind of cycles in kinship networks which result when spouses are linked to each other by ties of consanguinity or affinity. By taking a network-analytic perspective, the paper endeavours to put this classical issue of structural kinship theory on a general basis, such as to allow conclusions which go beyond isolated discussions of particular ring types (like "cross-cousin marriage", "sister exchange", and so forth). The paper provides a definition and formal analysis of matrimonial rings, a method of enumerating all isomorphism classes of matrimonial rings within given genealogical bounds, a series of network-analytic tools -- such as the census graph -- to analyse ring structures in empirical kinship networks, and techniques to effectuate these analyses with the computer program pajek. A program package containing the required macros can be downloaded from the web. The working of the method is illustrated at the example of kinship networks from four different parts of the world (South-America, Africa, Australia and Europe).

  Key words: Matrimonial rings, kinship, social network analysis, graph theory, enumeration theory, social anthropology

  2007 Douglas R. White and Woodrow W. Denham The Indigenous Australian Marriage Paradox: Small-World Dynamics on a Continental Scale, Mathematical Anthropology and Cultural Theory. Guest edited by David Kronenfeld and archived at UC eRespositories. See further analysis of these data by members of the machine learning team at the MIT Department of Brain and Cognitive Sciences: Kemp, C., Griffiths, T. L. & Tenenbaum, J. B. (2004) Discovering latent classes in relational data. AI Memo 2004-019 (pdf) - see Part 4 on blocking Alyawarra kin terms ckemp at MIT.edu

  Abstract: Ethnographies of Indigenous Australian language groups suggest that their populations were consistently small, averaging perhaps 500 people each, while classical models of their kinship systems consistently embody endogamous marriage as both a norm and a logical requirement. However, paleodemographers argue that reproductively closed small human populations are doomed due to stochastic variations in birth rates and sex ratios, while geneticists are similarly concerned about the potentially lethal effects of inbreeding depression in small populations. How then did these societies avoid extinction and indeed persist in Australia for 40,000 years and more? We introduce a mathematical model of Aboriginal descent, marriage and kinship that is reproductively open rather than closed, show how the openness articulates with traditional closed models, and demonstrate how the resulting system might maintain dynamic population stability despite internal and external stresses that might otherwise lead to extinction. The mathematical model demonstrates how each language group creates and maintains a local cluster in the space of a large "small world" of continent-wide marriage connections.

2005 Woodrow W. Denham and Douglas R. White Multiple Measures of Alyawarra Kinship, Field Methods 17(1):70-101. Guest edited by Dwight Read. See further analysis of these data by members of the machine learning team at the MIT Department of Brain and Cognitive Sciences: Kemp, C., Griffiths, T. L. & Tenenbaum, J. B. (2004) Discovering latent classes in relational data. AI Memo 2004-019 (pdf) - see Part 4 on blocking Alyawarra kin terms ckemp at MIT.edu

Abstract: A field experiment conducted in Central Australia in 1971-72 explored differences between what Aborigines actually did and what they said they did when anthropologists interviewed them. Fieldwork entailed observing behavior and recording it in numerically coded forms; analysis entails extracting patterns computationally that would not appear in traditional ethnographic data. This paper focuses on discrepancies between expected and observed with regard to descent, marriage and kinship. First it examines field methods and the resulting dataset, then it reviews a wide range of analytical methods that have been used to interpret the data. The alternative analytical methods reviewed here serve to test "competing hypotheses" about the nature and operation of Alyawarra descent, marriage and kinship. At the same time, however, the cumulative result of using these diverse methods has been increasingly complex and subtle understandings of previously unknown aspects of Central Australian social organization. The fact that the data continue to repay increasingly sophisticated analyses thirty years after they were recorded attests to the success of the field experiment.

Conclusions:

• The Radcliffe-Brown normative model functions as a kind of "cognitive core" for the Alyawarra system of descent, marriage and kinship. It is not incorrect, but it is seriously incomplete and inadequate.
• Examination of alternate models of Alyawarra social struWorkshop on Dynamics of groups and institutions: Their emergence, co-evolution and environment. Santa Fe Institute and the Research Centre of the Slovenian Academy of Sciences, from June 7 to June 11, 2004cture cannot be uniquely resolved into a single model but a nested model with a unique simplest structure embedded in models that are more complex. Each layer of models conforms to actual marriages that are in 98% agreement with the RB section memberships.
• The elegance of the Atkins' double helix model is marred by the fact that patterns of marriage among the deceased are quickly forgotten and no longer cast their shadow as a constraint on future behaviors. Thus the "kinship system" can evolve dynamically across a class of network models influenced stochastically by age distributions at marriage in accordance with Tjon Sie Fat's algebraic model, and to incorporate non-Alyawarra lineages in ways that are incompatible with both the RB and the Atkins models, thereby violating the Axiom of Algebraic Closure. An open format model that does not require the assumption of Generational Closure is one of the nested models that provide a good fit to the ethnographic data.
• The problem posed by the widespread extra-normative application of Omaha terms led us to discover recurring patterns in Alyawarra behavior that give the people a great deal of discretionary control over marriage by applying Omaha terms non-reciprocally in violation of the Axiom of Universal Reciprocity.
• Not only was the field experiment successful, but our findings require some fundamental rethinking of models for Australian kinship.

2002 Douglas R. White and Michael Houseman The Navigability of Strong Ties: Small Worlds, Tie Strength and Network Topology, in Networks and Complexity Special Issue, Complexity 8(1):72-81. Santa Fe Institute Working Paper eScholarship Reprint

Abstract: We examine data on and models of small world properties and parameters of social networks. Our focus, on tie-strength, multilevel networks and searchability in strong-tie social networks, allows us to extend some of the questions and findings of recent research and the fit of small world models to sociological and anthropological data on human communities. We offer a ***navigability of strong ties*** hypothesis about network topologies tested with data from kinship systems, and potentially applicable to corporate cultures and business networks.









2004 Douglas R. White Network Analysis and Social Dynamics. Cybernetics and Systems 35(2-3):173-192, online journal, special issue. Edited by Dwight Read. Introduction by Murray Leaf Session papgers: Mathematical Modeling and Anthropology: Its Rationale, Past Successes and Future Directions Dwight Read, Organizer, European Meeting on Cybernetics and System Research 2002 (EMCSR 2002)

Abstract. Network analysis, an area of mathematical anthropology and sociology crucial to the linking of theory and observation, developed dramatically in recent decades. This made possible a new understanding of social dynamics as a synthesis of network theories. Concrete links can be identified between the actions of self-reflective agents, with rich information processing and decision processes deeply embedded in social worlds, and emergence or change in the self-restructuring systems they operate -- including the emergence of organizations, groups, institutions, norms and cultures.

1998 Michael Houseman and Douglas R. White, Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya. Kinship, Networks and Exchange, Chapter 4, pp. 58-88. Edited by Thomas Schweizer and Douglas R. White. Cambridge: Cambridge University Press. Article reviewed in Kinship, Computing, and Anthropology pdf

Abstract. Edmund Leach's data on kinship and marriage is the starting point for a network analysis of marriage exchange and the bilateral devolution of property. The analysis resolves the "Dravidian controversy" over the possibility of fit between the egocentric perspective of dual organization encoded in the Dravidian languages of South Asia and a sociocentric dual organization that is NOT based on matrimonial moieties and unilineal descent, but a more flexible and network-based application of marriage strategies. A network concept of "sidedness" is developed as a new alternative to the moiety concept for dual matrimonial organization. In a significant number of cases where Pul Eliyan villagers marry cousins or other types of consanguineal kin, perfect sidedness is maintained in the actual network of kinship and marriage relations, consistent with the Dravidian "two-sided" terminology of direct matrimonial exchange. Agnatic descent, however, is not the principle by which sidedness is maintained, since daughters can be heirs to agnatic estates if male heirs are lacking, and there exists a significant option of propertied daughters taking the role of a male in the marriage exchange system. Alongside the normal rule of postmarital residence with the husband's agnatic kin, there exists the uxorilocal alternative that is emphasized by Leach as having strategic importance for marriage alliances between affines. Such marriages, when they involve transmission of agnatic property to the daughter (in the absence of sons), provide the key to understanding how an emergent network structure of dual organization is possible based on flexible marriage strategies rather than prescriptive descent rules for matrimonial moieties. The result is that while blood marriages follow the prescriptions of Dravidian "two-sided" kinship terminology, more strategically oriented marriages may ignore the implications of Dravidian terminology when it comes to marriages between strictly affinal kin, agnatic heiresses marrying men from remote villages, or blood relations through men from remote villages. While certain of these marriages are recognized as "wrong" from a terminological standpoint, the ideal of a consistent but continually re-emergent sociocentric dual organization is superimposed on the behaviorally "wrong marriages." The only casualty of this emergently networked dual organization is the anthropological insistence that dual organization is necessarily dependent on rules of descent. For Pul Eliyans, however, "sidedness" is resolved case by case with the social validation of successive marriages, and not rationalized with respect to a formal logic of descent.

Here then is a system of social rules and strategies that are reconciled against each other in the freedom to realign and readjust terminological discrepancies in favor of a continually reemergent but consistent network structure of dual matrimonial organization that lacks a basis in a strict rule of descent. The rules of bilateral inheritance, it turns out, have more significance for property-holding residential groups than the rules of descent. Furthermore, property that is temporarily alienated from an imperfectly agnatic residential group because of inheritance devolution to daughters can be brought into the group through the combination of subcaste endogamy and dual organization in which "agnatic" property devolving through females can first pass to an opposing "side" but then back to its "side" of origin. Disputes about legitimate claims to agnatic property are common in this exchange system, but form an integral part of the emergent process by which there are micro-level changes to the structure of dual organization whose practical effect is to support an ethos of balanced exchange between equal but opposing "sides" -- the key feature of Dravidian-type social and economic organization.

1996 Michael Houseman & Douglas R. White, Les structures reticulaires de la pratique matrimoniale. L'Homme 139: 59-85

Abstract. This article proposes a new approach to the comparative study of alliance systems, centered on the dynamic coordination of actual marriage choices. With the aid of diverse software tools, the authors seek to identify the emergent properties of matrimonial networks as a whole ensemble. After explaining some of the methodological aspects of this work, they present two relatively simple network characteristics, ones that correspond to two modalities of bipartition of the nodes in the network: one the structure of dividedness, the other that of sidedness. Certain more general theoretical perspectives on bipartite marriages networks are envisaged.

1998 Douglas White & Thomas Schweizer, Kinship, Property Transmission, and Stratification in Javanese Villages. Kinship, Networks and Exchange, Chapter 3, pp. 36-58. Edited by Thomas Schweizer and Douglas R. White. Cambridge: Cambridge University Press.

Abstract. This paper analyzes ethnographic data on kinship, transmission of land and religious activities among elite Muslim families in a Javanese village, against a background of Javanese kinship ethnography and comparisons with kinship networks of village hamlets and elites in other villages. Concomitant variation establishes support for general hypotheses about the organization of Javanese kinship. Parental graph analysis (White and Jorion 1992) is used for network comparisons and to focus on processes of transmission and consolidation of resources among the elites, and establishes subsets of actors connected by common bilateral descent and marriage ties. Inheritance of land, religious activities and ensuing occupational specialization can be closely traced as secondary flows on the basic kinships scaffolding. Stern's (1994) visual algebra is used for representing and breaking down subsets of actors or ties and for creating images of the whole network. The discrete methods applied in this paper are precise tools for decomposing multiple ties in kinship networks and yield deeper insight into structural patterns than standard methods of positional analysis tried in an earlier paper (Schweizer 1988).

2004 Douglas R. White, Cross-Cultural Research: An Introduction for Students, World Cultures 14#2:164-178. early version

Abstract. Cross-tabulations of qualitative data are a fundamental tool of empirical research. Their interpretation in terms of testing hypotheses requires a number of relatively simple concepts in statistical analysis that derive from probability theory. When strictly independent events having two characteristics that are independently defined are tabulated in a contingency table, the laws of probability can be used to model, from the marginal totals (rows, columns) of the table, what its cell values would be if the variables were statistically independent. The actual cell values of the frequency table can be used to measure the correlation between the variables (with zero correlation corresponding to statistical independence), they can be compared to expected values under the null hypothesis of statistical independence, and they can be used to give an significance-test estimate of the probability that the departure of the observed correlation from zero (statistical independence) is simply a matter of chance. Further, when the sample of observations departs from strict independence because of observed interactions between them, the correlations between interacting neighbors measured on the same variables can be used to deflate effective sample size in obtaining accurate significance tests.

2004 Douglas R. White, A Student's Guide to Statistics for Analysis of Cross-Tabulations, World Cultures 14#2:179-193. update

Abstract. To answer the need for a simplified and comprehensive introduction to Cross-Cultural Research in the context of a classroom in a computer laboratory, this introduction addresses

• 1 What is Cross-Cultural Research? (with a focus on Cultural coherence or decoherence within and between human communities: human behavior, beliefs, and institutions)
• 2 A Course in Cross-Cultural Research
• 3 Goals and Outcome
• 4 Tools: Spss; Maps and MapTab; Statistics for Galton's Problem
• 5 Topics and Terms: Lists of Topics; Files; References; Glossary
• 6 Resources: e.g., on-line articles, e.g., JSTOR "Polygyny"
• 7 Draft and Final Paper
• 8 References
• 9 On-line Resources:

  Articles from World Cultures journal at http://www.worldcultures.org/

  [2002] 1969 George P. Murdock and Douglas R. White, Standard Cross-Cultural Sample: on-line. Reprinted with new annotations from Ethnology 8:329-369

  Abstract. Since 1969, hundreds of cross-cultural studies have contributed coded data using the Standard Cross-Cultural Sample which is now reprinted here with annotations and guides to the on-line database as published in World Cultures.

  See also, 2006: Pinpointing Sheets for the Standard Cross-Cultural Sample Douglas R. White and George P. Murdock

  SCCS Wikipedia site

  SCCS and Related articles

  1968. Douglas R. White, Societal Research Archives System: Retrieval, Quality Control and Analysis of Comparative Data Social Science Information 7(3): 78-94.

  1969. Douglas R. White, Cooperation and Decision Making among North American Indians Ann Arbor, MI: Dissertation Reprints.

  1985. Douglas R. White, Process, Statistics and Anthropological Theory: An Appreciation of Harold E. Driver Reviews in Anthropology 2:295-314. Driver, Harold E. 1966. An integration of functional, evolutionary and historical theory by means of correlations. Indiana University Publication in Anthropology and Lingujistics, Menoir 12.

  [2002] 1986 Douglas R. White, Data Base . Current Anthropology 27(1):83-84

  Abstract. Since 1969, hundreds of cross-cultural studies have contributed coded data using the Standard Cross-Cultural Sample which will now distributed in the journal World Cultures.

  1990 Douglas R. White, Reliability in Comparative and Ethnographic Observations: The Example of High Inference Father-Child Interaction Measures, Journal of Quantitative Anthropology 2: 109-150,

  Abstract.The theory of reliability and reliability estimates, nearly a century old, has rarely been employed in anthropology, both for lack of familiarity and related problems of computation. This theory is reviewed and considered for use with anthropological data. A set of procedures is provided which combine existing methods to solve the practical problems in use of the theory to assess the reliabilities of composite measurement scales combining multiple measures, of individual independent measurements of a single concept, and of individual cases scored on the composite scales. These procedures are also embodied in a computer program, the results of which are explicated. While domain sampling assumptions are the only requirements of assessing reliability of composite scales, strict assumptions and validation procedures are discussed for the assessment of individual variable reliabilities. An illustration using reliability theory is drawn from cross-cultural studies for "high inference" measures from four different studies of father - child interaction. Validity issues are illustrated both in terms of tests for measurement bias and construct validity for the hypothesized relation between the father - child bond and beliefs in high gods.
  Reliability theory is equally applicable in comparative and ethnographic case studies. It offers research practices and theoretical understandings that are capable of integrating and mediating discourse between many of the splintered schools of thought in anthropology, and healing some of the rifts between them. Essentialist biases are discussed as one reason why the theory is not more, widely employed.

  1997 Douglas R. White and J. Patrick Gray, Corr-Rel: A Program for Reliability Assessment. World Cultures 9(1): 58- 75. Corr-Rel pdf

  Abstract. A co-authored methodological guide to software written by the first author assesses the classical problems (discussed by White 1990) of determining (1) unidimensionality of multiple measures of the same construct as a prerequisite to assessing reliability, (2) item and multiple-item scale reliability and (3) the reliability of estimates for individual cases.

  1986 Douglas R. White, Focused Ethnographic Bibliography for the Standard Cross-Cultural Sample: on-line. World Cultures 2(1):1-126.

  Abstract. Since 1969, hundreds of cross-cultural studies have contributed coded data using the Standard Cross-Cultural Sample. The bibliography is a coded compendium of all the ethnographic sources used in different coding projects by hundreds of contributors. Relevance to the pinpointed ethnographic site and time period is coded for each ethnographic source. The on-line database is published in World Cultures.

  

  1993 Douglas R. White, Spatial Levels in Cultural Organization: An Empirical Study. Handbuch der Ethnologie, pp. 459-88. Edited by Thomas Schweizer, Margarete Schweizer, and Waltraud Kokot. Berlin: Reimer Verlag.

  Abstract. Interpreting comparative observations from diverse world cultures poses the dilemma of how to unfold the wide variety of functional and historical processes observed in cultural systems. Do correlations among cultural variables represent functional relations or historical adhesions? Some elements are acquired through independent invention (including functional adaptation), others through common origin (through migration, replication of like units) or diffusion (borrowing between units). Diverse origins may indicate differing functions or explanations for cultural phenomena, but functions also change in time and may require different explanations under the selective pressures of a different historical period. Similar institutions among cultures at one point in time may reflect convergent adaptation and historical interaction rather than commonality of origin.

  The present article adopts the spatial perspective on the patterns of similarity and differences between culture-bearing entities, using a measure of spatial autocorrelation, the Moran coefficient (Moran 1950). An overall index of spatial clustering in cultural patterns is estimated from the application of spatial autocorrelation statistics to cross-cultural data. Autocorrelation - the measure of similarity among related units - has a direct relevance to comparative research in that it has profound methodological implications for testing cross-cultural hypotheses that depend on measuring correlation between variables. E v a with small samples (e.g., of N=40), levels of autocorrelation of .40 and above are sufficient to cause serious underestimate, by orders of magnitude (e.g., at half or less of the true value) of sample variance, standard errors, and confidence limits @ow, Burton and White 1982), both for sample means and estimates of correlation or regression coefficients.

  Leaving methodological issues aside, at least until results of the study on levels of autocorrelation are presented, the spatial organization of culture is necessarily a major theoretical issue in anthropology if there are mnltiple processes in cultural systems that work at different spatial levels and time scales.

  1995 Douglas R. White, George Peter Murdock American National Biography Oxford University Press under the auspices of the American Council of Learned Societies. On line edition at http://www.anb.org

  1990 Douglas R. White, World-system and regional linkages as causally implicated in local level conflicts at the ethnographic horizon. Zeitschrift fur Ethnologie 115: 111-134.

  Abstract. Critique of dispositional explanations for local level conflict shows anomalies in Ross's (1985) theory of violence and in ethnographic accounts using "culture of violence" explanations of conflict. This paper parallels international relations theories (e. g. Waltz 1959) in examining hypotheses about regional and world-system linkages as causally implicated in local-level warfare. In a pilot study using a fraction of the standard sample, two variables are found to predict external conflict: Frequency of interregional contact and relocation forced by powers in the larger world-system. The correlation between external and internal conflict is positive in more peripheral zones of the world-system, but negative in the more central zones. External war combined with the extent of state level organization predicts the strength of fraternal interest groups, one of the dispositional predictors of internal violence. Such evidence might support a scenario for reversing the direction of causation in Ross's theory of violence such that internal violence and societal features "disposing" to internal violence (including features of socialization) may result from conflictual pressures at the world-system, regional linkages and state levels.

  These findings support Ross's (1985: 553-554) statement that "As a number of modern nations haves shown ..., teaching a citizenry to fight outside enemies often produces more fighters inside as well." They do not support his speculation that "Similarly, if violence is a mechanism for dealing with internal opponents, whv would we not expect it to he used with outsiders too?" simply because internal violence almost never occurs independently of external war, which makes a reversal of causality implausible.

  2002 Ulla Johansen and Douglas R. White, Collaborative Long-Term Ethnography and Longitudinal Social Analysis of a Nomadic Clan In Southeastern Turkey . Chapter 4, pp. 81-99, in Chronicling Cultures: Long-Term Field Research in Anthropology, edited by Robert van Kemper and Anya Royce. AltaMira Press. Book Review

  Abstract. Longitudinal network analysis is coupled in this study to a systematic analysis of the results of long-term ethnography of a nomadic group. Data collection using genealogical, interview and observational methods is complemented by analytic methods using graph theoretic concepts and dynamical as well as structural methods to assess various cross-cutting and hierarchical levels of social cohesion (nuclear and extended families, lineages, clans, tribal groups, and village or nationality affiliations as found within the nomad group) to formulate and test hypotheses about social mobility and political leadership. Predictive hypotheses about the inverse relation between out-mobility and social cohesion versus the direct relation between cultural transmission and marital relinking as a form of cohesion are thought to validate the basic approach. The model of distributed cohesion developed from these data provides a new understanding of processes supporting the emergence of leaders in egalitarian nomadic groups.

  

  2001 Douglas R. White and Frank Harary, The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density. Sociological Methodology 2001, vol. 31, no. 1, pp. 305-359. Blackwell Publishers, Inc., Boston, USA and Oxford, UK. cited in Annual Review of Sociology 2004 SFI-WP2004-03-09 SFI Posting

  Abstract. This study shows various ways that formal graph theoretic statements map patterns of network ties into substantive hypotheses about social cohesion. If network cohesion is enhanced by multiple connections between members of a group, for example, then the higher the global minimum of the number of independent paths that connect every pair of nodes in the network, the higher the social cohesion. The cohesiveness of a group is also measured by the extent to which it is not disconnected by removal of 1, 2, 3,..., n actors. Menger's Theorem proves that these two measures are equivalent. Within this graph theoretic framework, we evaluate the family of concepts of cohesion and establish the validity of a pair of related measures:
  1. Connectivity - the minimum number k of its actors whose removal would not allow the group to remain connected or would reduce the group to but a single member - measures the social cohesion of a group at a general level.
  2. Conditional density measures cohesion on a finer scale as a proportion of ties beyond that required by a graph's connectivity k over the number of ties that would force it to k + 1.

  Calibrated for successive values of k, these two measures combine into an aggregate measure of social cohesion, suitable for both small-and large-scale network studies. Using these measures to define the core of a new methodology of cohesive blocking, we offer hypotheses about the consequences of cohesive blocks for social groups and their members, and explore empirical examples that illustrate the significance, theoretical relevance, and predictiveness of cohesive blocking in a variety of substantively important applications in sociology.

  2001 Frank Harary and Douglas R. White P-Systems: A Structural Model for Kinship Studies. Connections 24(2):35-46. Click article title at that site for the PDF.

  Abstract: Several mathematical models have been proposed for kinship studies. We propose an alternate structural model designed to be so simple logically and intuitively that it can be understood and used by anyone, with a minimum of complication. It is called a P-system, which is short for parental system. The P-system incorporates the best features of each of the previous models of kinship: a single relation of parentage, graphs embedded within the nodes of other graphs, and segregation of higher level descent and marriage structure from nuclear family structure. The latter is also the key conceptual distinction used by Lévi-Strauss (1969) in the theory of marriage alliance. While a P-system is used to represent a concrete network of kinship and marriage relationships, this network also constitutes a system in the sense that it contains multiple levels where each level is a graph in which each node contains another graph structure. In sum, the connections between the nodes at the outer level in a P-system are especially useful in the analysis of marriage and descent, while at inner level we can describe how individuals are embedded in the kinship structure.

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  ENTAILMENT ANALYSIS (click here for software) AND MATHEMATICAL ANTHROPOLOGY

  1977 Douglas R. White, Michael L. Burton, and Lilyan A. Brudner, Entailment Theory and Method: A Cross-Cultural Analysis of the Sexual Division of Labor. Cross Cultural Research 12:1-24. original draft
  download data from spss excel

  Abstract. The purpose of this paper is to explore a more precise form for theoretical propositions in certain types of cross-cultural problems and to develop and explicate an accompanying statistical method. An inductive application of the method for entailment analysis has led us to formulate a new and powerful theory of the sexual division of labor.

  1983 Douglas R. White, Robert Pesner, Kark Reitz, An Exact Significance Test for Three-Way Interaction Cross Cultural Research: 18:103-122.

  Abstract. A modification of Fisher's exact test for the 2 x 2 x 2 contingency table is proposed as a test of the null hypothesis of no three-way statistical in teraction among variables, controlling for the two-way or first-order correlations. The test uses a truncated hypergeometric distribution, limited by the bivariate marginal totals of the variables. Possible generalizations to L x M x N tables are discussed. The test is also applicable to the null hypothesis of no difference in the magnitude of correlation in a comparison of two bivariate distributions. Illustrations of each application are provided. One obvious use in cross-cultural or survey research is as a test of the replication of a correlation in different subsamples of a population.

  This test, for binary variables, is used prior to entailment analysis to verify the absence of greater-than-random occurrence of higher-order interactions.

  1988 Douglas R. White and H. Gilman McCann, Cites and fights: material entailment analysis of the eighteenth-century chemical revolution SOCIAL STRUCTURES: A Network Approach, Edited by Barry Wellman and S.D. Berkowitz. New York: Cambridge University Press

  Abstract. Statistical entailment analysis (White, 1984; White and McCann, 1988 Social Structures: Form and Behaviour in Social Life) (Cambridge University Press) pp. 380-404) aims first at a rigorous evaluation of null hypotheses of statistical independence as a potential source of binary data structure, and second at constructing a discrete structure (Boolean) model of those statistical interactions that remain when the null hypothesis is rejected for particular subsets of variables. Signal detection theory, rather than a conventional significance level, is used to specify optimal cutoffs given an ordering of ratios of actual to expected across levels of exception and relevance. Bivariate entailment analysis is generalized here to improve its utility for use in lattice approximation. Generalized statistical entailment analysis describes Boolean patterns in a set of data in terms of those that occur with greater frequency than expected by chance according to a model of complete statistical independence (the specific model of independence derives from a distribution of randomly permuted entries in the columns of the data matrix marginals, i.e. keeping univariate marginals fixed). This expands on the initial design of entailment analysis (White, 1984) to deal with partial orders of quasi-implication in pairs or chains of dichotomous variables, supported by statistical evidence of departure from bivariate independence and conformity to the rules of transitivity. Statistical approximations simplify a lattice representation of discrete structure by forcing quasi-implications (ignoring exceptions), for example, but they also provide information about those implications in the lattice that represent statistically significant tendencies. Given a lattice representing the discrete structure of a raw data matrix, the findings of entailment analysis describe additional structural regularities (tendencies towards further statistical constraints on Boolean patterns that occur in the data) that can be used to simplify (by approximation) the lattice of empirical patterns. As demonstrated with studies of dual orderings of material possessions (possessions stratify people; people possessions), the statistical interpretability of discrete structure lattices is enhanced by using the results of entailment analysis for consensus-simplification of statistically strong or significant implicational relations.

  2000 Douglas R. White Manual for Statistical Entailment Analysis. World Cultures 11(1):77-90.

  A programmed statistical method developed for the analysis of binary data by the author explicates how to find approximations to discrete Boolean relations of inclusion, mutual exclusion, and collective exhaustion that satisfy empirical conditions for transitivity, and thus which facilitate formulation of rules and generalizations in discrete form ("If ... then ...") that are also logically transitive. Signal detection methods are used to reject relationships that could be due to chance by comparing actual relationships to those found in Monte Carlo simulations of comparable random datasets. The analytic results constitute a discrete network structure of nontrivial empirical implications that characterize a dataset.

  1996 Statistical entailments and the Galois lattice Douglas R. White. Special Issue on Social Network and Discrete Structure Analysis Social Networks 18(3): 201-215. doi:10.1016/0378-8733(95)00273-1 Copyright (c) 1996 Published by Elsevier Science B.V.

  Abstract: Statistical entailment analysis (White, 1984; White and McCann, 1988 Social Structures: Form and Behaviour in Social Life) (Cambridge University Press) pp. 380-404) aims first at a rigorous evaluation of null hypotheses of statistical independence as a potential source of binary data structure, and second at constructing a discrete structure (Boolean) model of those statistical interactions that remain when the null hypothesis is rejected for particular subsets of variables. Signal detection theory, rather than a conventional significance level, is used to specify optimal cutoffs given an ordering of ratios of actual to expected across levels of exception and relevance. Bivariate entailment analysis is generalized here to improve its utility for use in lattice approximation. Generalized statistical entailment analysis describes Boolean patterns in a set of data in terms of those that occur with greater frequency than expected by chance according to a model of complete statistical independence (the specific model of independence derives from a distribution of randomly permuted entries in the columns of the data matrix marginals, i.e. keeping univariate marginals fixed). This expands on the initial design of entailment analysis (White, 1984) to deal with partial orders of quasi-implication in pairs or chains of dichotomous variables, supported by statistical evidence of departure from bivariate independence and conformity to the rules of transitivity. Statistical approximations simplify a lattice representation of discrete structure by forcing quasi-implications (ignoring exceptions), for example, but they also provide information about those implications in the lattice that represent statistically significant tendencies. Given a lattice representing the discrete structure of a raw data matrix, the findings of entailment analysis describe additional structural regularities (tendencies towards further statistical constraints on Boolean patterns that occur in the data) that can be used to simplify (by approximation) the lattice of empirical patterns. As demonstrated with studies of dual orderings of material possessions (possessions stratify people; people possessions), the statistical interpretability of discrete structure lattices is enhanced by using the results of entailment analysis for consensus-simplification of statistically strong or significant implicational relations.

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  1983 Douglas R. White and Karl P. Reitz, Graph and Semigroup Homomorphisms Social Networks 5:193-234.

  2000 Douglas R. White and Karl P. Reitz, Homomorphismos de grafos y semigrupos sobre redes de relaciones. Politica y Sociedad 33:149-165. [Reprint in translation of 1983 "Graph and Semigroup Homomorphisms" Social Networks 5:193-234. ]

  A set of nodes in a graph are regular-equivalent when each has the same relations with other nodes that are regular-equivalent. For a homomorphic mapping (or blockmodeling) of nodes and arcs into an image that preserves adjacencies, regular equivalence offers the structure-preserving property that semigroups of generating and compound relations on the original graph (or network with multiple kinds of arcs or edges) are preserved.

  1999 Douglas R. White, Vladimir Batagelj and Andrej Mrvar, Analyzing Large Kinship and Marriage Networks with Pgraph and Pajek, Social Science Computer Review 17(3):245-274. Sage Article

  The p-graph approach that has proven an invaluable aid to the study of kinship, marriage and genealogical network analysis here is explicated ñ in terms of solving five key conceptual problems of network studies, including that of identifying subgroup boundaries -- and combined with a computer package for sparse-network algorithmic analysis and visual representation of large (up to 90,000 node) networks. The results of this new marriage between graph-theoretical analysis, computer science, network anthropology and network-visualized social history are illustrated for a 1600- person social system consisting of an entire Turkish nomad society, with a relinking density of 75%, the highest density of structural endogamy yet recorded. It is shown how the algorithmic, analytic and graph-editing technology of this new concatenation of elements for network analysis leads to striking new understandings of social structure and social processes, and how to prepare visualizations of discoverable emergent properties of structure in such a large and dense network. This article reviews the developments and contributions of the authors to the evolution of these tools and methods for large-scale network analysis, and provides a complete series of guides and illustrations for the reader to utilize the two software packages discussed.

  1997 Douglas R. White, edited by Patricia Skyhorse, Parente Suite User's Guide. PGRAPH: Software for Kinship and Marriage Networks Website.

  The p-graph approach, now in wide use (see: KinSources), is documented in Parente Suite User's Guide. Out of print since 1999, it contains a tutorial "Six Steps for Kinship Graphs: from Genealogical Data to Network Analysis." It was superceded by standard p-graph options in 1999 Douglas R. White, Vladimir Batagelj and Andrej Mrvar, Analyzing Large Kinship and Marriage Networks with Pgraph and Pajek, Social Science Computer Review 17(3):245-274.

  1999 Douglas R. White, Networks, Cognition and Ethnography: Thomas Schweizer Remembered, Connections 22:19-27.

  Abstract: The life and research agenda of Thomas Schweizer, who died suddenly at the age of 48, is considered in terms of its contributions to anthropology and social science generally. Schweizer was the leading contributor to a processual approach to understanding the fundamentals of ethnographic research through a synthesis between the network approach to social organization and an actor based approach that takes into account cognition and individual decision making under the network constraints and dynamics of social organization. This memorial considers how this synthesis developed within Schweizer's career and his institutional and intellectual contributions to German Anthropology and the University of Cologne Institute of Ethnology.

  1997. Structural Endogamy and the Graphe de Parenté. Mathématiques, Informatique, et Sciences Humaines 137:107-125.

  Abstract. This article, one of a series, approaches the topics of marriage and kinship through a revitalized kinetic structural approach that shifts the primary focus from abstract models of rules, terminologies, attitudes and norms to exploration of concrete relations in a population, analyzed graph-theoretically in their full complexity as networks. Network representation using the graphe de parenté (p-graph) serves as the basis for examining marriage alliance theory, population structure (such as endogamy and exogamy, inbreeding, subgroups), as well as other possible concepts of general sociological interest. These include structural endogamy as a cohesive relational structure, which is associated with social formations such as classes, strata, ethnicity, and elites (Schweizer and White 1998, in press). This type of potentially multi-layered structural approach extends to the study of structures and processes of actual marriage and kinship practices and other forms of social linkage that build off of them. Identification of structure and processes which occur in such networks is enhanced by mapping attributes or dynamic variables onto the armature of the kinship graph. Any number of theoretical questions concerning kinship and marriage may be posed or restated to address questions of the structure of kinship networks, and thus depend upon such analysis for deeper critical insights. The focus in this discussion is specifically on the connections between graph-theoretic analysis and various substantive theoretical questions concerning kinship and marriage networks.

  1997 Lilyan A. Brudner and Douglas R. White. Class, Property and Structural Endogamy: Visualizing Networked Histories publisher posting: Theory and Society (Springer link) 26:161-208. (the repeated footnote number, 8, on p 164 should be 9). Reprinted at eScholarship
  Available at a library near you
  Feistritz genealogical index

  Abstract. This is the first theoretical application of the concept of structural endogamy as identifying an empirical variable or boundary condition within social networks that is linked in causal-explanatory ways to social class formation. Using an ethnographically rich case study of an Austrian village in which oral and (ca. 100) household genealogies provide 150 years of marriage network data, while manorial archives continue the stem-line household genealogies back to the founding of the "house system" in 1517, the hypothesis is formulated that the social class boundary between farmstead owner-operators (including heirs and buyers) and secondary service occupations not linked to farmstead ownership is established and maintained through the mechanism of structural endogamy. Two principles of inheritance are in conflict in this farmstead house-system, that of passing the principal productive property intact to a principal heir (usually a son, or if not is available, a daughter), and that of the intestate rights of children to equal division of parental inheritance. The use of wills or testaments resolves his conflict through "equitable division" which maintains stem-line impartibility of farmsteads along with quitclaims to those who are not principal heirs. Structural endogamy, in this case specifically the marriage of a potential heir to a spouse who brings in divided property from another divided patrimonial stemline, is shown to be (1) a qualification for class membership via principal heirship, (2) a means of reconstituting subdivided estates, and (3) a means of social perpetuation of the two-class system which often even divides siblings within the same nuclear family. The predicted statistical relationship between class-membership, heirship and structural endogamy is confirmed empirically and implications for new approaches to studies of social class formation are discussed.

  Reviewer comments. One paper, that by Brudner and White, does appear to break new methodological ground and seems to me to be distinguished on theoretical and historical grounds as well. The Brudner/White method for analyzing longitudinal large-scale social networks has perhaps solved a problem that has eluded the discipline for many years. Brudner and White go further than demonstrating a new method: they show that they can speak to and articulate with a broad range of classical and contemporary theoretical problems. This paper, previously published as well in Theory and Society, would warrant republication if there was no other published work describing this method. Of all the papers submitted for consideration, I found this one to be the freshest and most interesting, in part because it spoke to debates that are actually considered in the current theoretical landscape of sociology.

  Structure and Dynamics of the Global Economy: Network Analysis of International Trade 1965-1980 David A. Smith, Douglas R. White Social Forces, Vol. 70, No. 4. (Jun., 1992), pp. 857-893.jstor
  pw/GlobalEcon1992.pdf

Abstract: This article reports results from a quantitative network analysis of international commodity trade flows designed to measure the structure of the world economic system and to identify the roles that particular countries play in the global division of labor. It improves on previous network-analytic studies of the world economy in two ways. First, by using a newly developed measure of regular equivalence, this operationalization of a nation's roles in the international system is methodologically superior to previous work. Second, we have built a dynamic aspect into the analysis by examining international trade networks at more than one point in time (1965, 1979, and 1980). This allows us to answer questions about change both in the overall structure of the world-economy and in the positions of particular countries in the system. Our findings generally conform to the theoretical expectation of the world-system perspective as well as qualitative descriptions of recent changes in the international division of labor.

1988 Large-Scale Network of World Economy: Social scientists use the CRAY
Interview: Douglas R. White, David A. Smith. Science at the San Diego Supercomputer Center 1987: 27-28

Abstract. Two page summary of main results of Smith and White, 1992.

1988 Flow Centralities: Do they Predict the Economic Rise and Fall of States? Douglas R. White and David A. Smith. Paper for Sunbelt Meetings 1988 San Diego pub/White&Smith.pdf FIGURES

Abstract. The problem of measuring the centrality of states, and of explaining the economic rise and fall of states, is a central issue engaging social theorists accounting for social structure and change. The problem arises not only in recent times, but rather has always been a current one. Theorists tend to agree that long term macroscopic perspective is needed to situate the problem in a formal way. In this field, however, the problem has not been situated previously on the appropriate structural measurements. This paper develops a structural model of the economic rise and fall of states based on formal measures of flow centrality. Its wider concern is with the dynamics and consequences of differential position and centrality in exchange networks.


The Distribution of Avoidances in Human Societies: figure, page 5, Douglas R. White and Rudolf Wille, in, Lattice Theory and its Applications: In Celebration of Garrett Birkhoff's 80th Birthday 1995, by K. A. Baker, Garrett Birkhoff, and Rudolf Wille. Lemgo, Germany: Heidermann Verlag.

Abstract. A nested line diagram (concept lattice) is used to show the structure of avoidances from a cross-cultural study by Douglas R. White, as drawn by Rudolf Wille in his "Lauditorio" to Professor Birkhoff, the American mathematician, author of Lattice Theory, which appeared in 1940, and, with Saunders Mac Lane 1997, A Survey of Modern Algebra.

The distribution of avoidances in human societies shows three fundamental dimensions: husband's affines (virilateral, starting with husband's father), wife's affines (uxorilateral, starting with wife's mother), and generalized affines (starting with wife's brother's wife and extending to opposite sex siblings). The last of the three independent dimensions of the distribution is a significant exception to the 'extensionist' theory of kinship, in which terminologies and characteristic behaviors are 'extended' from closer relatives to more distant relatives. In this case, avoidance behavior in the third dimension is extended from affines (WiBrWi) to close relatives (siblings), not the other way around.

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Some of the following articles in pdf format are found at JSTOR, for which you will need access from campus or your library password:
http://www.jstor.org/search/cc99331a.10221690180/1-6?configsortorder=SCORE&frame=noframe&dpi=3&config=jstor



Using Galois Lattices to Represent Network Data Linton C. Freeman, Douglas R. White Sociological Methodology 1993 (23):127-146. jstor
pw/Galois.pdf TypoP132Freeman_White.pdf . cited in Annual Review of Sociology 2004.

Abstract. Galois lattices are introduced as a device to provide a general representation for two mode social network data. It is shown that Galois lattices yield a single visual image of such data in cases where most alternative models produce dual images. The inzage provided by the Galois lattice produces, moreover, an image that can suggest useful insights about the structuralproperties of the data.

An example, based on data from Davis, Gardner, and Gardner (1 941), is used to spell out in detail the kinds of structural insights that can be gained from this approach. In addition, other potential applications are suggested.

Representing and Computing Kinship: A New Approach Douglas R. White, Paul Jorion Current Anthropology, Vol. 33, No. 4. (Aug. - Oct., 1992), pp. 454-463. jstor
For FEMALE LINKS in Fig. 2 please see: pw/White-Jorion1992.pdf

Abstract.

Rethinking Polygyny: Co-Wives, Codes, and Cultural Systems Douglas R. White Current Anthropology, Vol. 29, No. 4. (Aug. - Oct., 1988), pp. 529-572. jstor
pw/Polygyny1988.pdf

Abstract. A new set of codes is offered to begin to unpack the dimensions of polygyny. Included are measures of frequency and statistical distributions of multiple wives, cultural rules, residential arrangements and kin relations among co-wives, male stratification, and marriage of captured women. Problems of coding and measurement are extensively illustrated. A series of hypotheses is supported regarding two types of polygyny: wealth-increasing and sororal. In the first, women's labor generates wealth and (if warfare allows) female captives are taken as secondary wives. Here polygyny stratifies males by wealth and most men are able to become polygynists with age. Residential autonomy of wives is an elaboration of this pattern. The second is marked by coresidence of husband and wives and dependence of the family mostly on resources generated by the husband. Here polygyny is usually dependent on the exceptional productivity of particular men such as hunters or shamans. The regional-historical adaptations of these types differ markedly. Neither fits the model of resource-defense polygyny found in other species. Explanations of polygyny, particularly of the first type, require close attention to resource and demographic flows within regional ecologies. The second type requires further functional and historical analysis. Both require more consideration of the way polygyny operates from the female point of view, a task only partially begun here.

The Shared Workstation Applications Project (in Reports) Douglas R. White Current Anthropology, Vol. 29, No. 3. (Jun., 1988), pp. 519-520. jstor
pw/SWAP1988.pdf

Abstract.

Cross-Cultural Surveys Today Michael L. Burton, Douglas R. White Annual Review of Anthropology, Vol. 16. (1987), pp. 143-160. jstor
pw/XCS1987.pdf

Abstract.

1988. Causes of Polygyny: Ecology, Economy, Kinship, and Warfare. Douglas R. White; Michael L. Burton. American Anthropologist, New Series, 90(4):871-887. Stable URL: http://www.jstor.org/pss/680762 pdf

Abstract: We discuss and test competing explanations for polygyny based on household economics, malecentered kin groups, warfare, and environmental characteristics. Data consist of codes for 142 societies from the Standard Cross-Cultural Sample, including new codes for polygyny and environmental characteristics. An explanatory model is tested for the worldwide sample using regression analysis, and then replicated with regional samples. We obtain convergent results with two different measures of polygyny, cultural rules for men's marriages and the percentage of women married polygynously. We conclude that the best predictors of polygyny are fraternal interest groups, warfare for capture of women, absence of constraints on expansion into new lands, and environmental quality and homogeneity.

Network Autocorrelation: A Simulation Study of a Foundational Problem in the Social Sciences. Malcolm M. Dow, Michael L. Burton, and Douglas R. White. Social Networks 4(2):169-200. (June 1982)

Abstract: It is axiomatic to the social sciences, and an essential part of the network perspective, that human performances are intricately linked with their social and enviromental contexts. Researchers in each of the disciplines have rediscovered this in the past decade with respect to a whole host of specific problem areas, under such labels as "context effects", "index utility". and "systems analysis". The earliest mention of the problem with respect to quantitative research occured, to our knowledge, in the debate between the nineteenth century cultural diffusionists and the evolutionists. The latter regarded individual societies as independent instances of uniform causation, and hoped to learn about causation from correlational studies. The former regarded their observations as embedded in an interactive network of historical relationships such as diffusion, migration, conquest, and competition, where the historical, evolutionary and ecological context of each society and the network of interconnectedness between societies plays a major role in multiple causation. In this view, events cannot be regarded as isolated or independent as if each were a context-free "independent invention" of a single society.

The same arguments, of course, apply to the interpretation of data collected in social or opinion surveys. Political science offers a recent example of the discovery of "context effects" in voting behavior (e.g. Jackson 1975). How much of voting behavior is affected by attributes of the voting unit (whether individuals or aggregates), and how much is the result of interactions between them: of the communication process, bandwagon effects, reference group behavior, or other forms of "symbolic interactionism"?

Our purpose in this paper, however, is not to attempt a review of the vast literature on context effects. Rather, we focus on the costs and benefits of either neglecting context or else incorporating it in the research design. Statistical methods such as multiple regression analysis necessarily contain mathematical axioms which either assert or deny the existence of context effects. We will explore here through simulation studies the following related questions:
(1) What are the consequences of ignoring context effects, should they be present, or ordinary least squares regression estimates, and
(2) what are some of the properties of a recently developed maximum likelihood procedure which permits context effects to be included in a regression model as network autocorrelated disturbance terms?

1984. Galton's Problem as Network Autocorrelation. Malcolm M. Dow; Michael L. Burton; Douglas R. White; Karl P. Reitz. American Ethnologist 11(4), Social Structure and Social Relations. pp. 754-770. Stable URL: http://www.jstor.org/pss/644404

Abstract: Classical statistical inference procedures usually assume the independence of sample units. However, the assumption of independence is often unrealistic in cross-cultural research because societies in neighboring or historically related regions tend to be duplicates of one another across a wide variety of traits that are spread by historical fission, diffusion, or migration of peoples. A recent generalization of the usual regression model explicitly allows for networks of interdependencies among sample units as part of the model specification. Here, two new estimation procedures for this network autocorrelation model are compared to previously employed maximum likelihood procedures, and to the usual regression procedures which ignore interdependence. The results of comparisons based on simulated autocorrelation data and the reanalyses of two previously published empirical studies indicate that both of the procedures proposed here compare very favorably with the maximum likelihood approach, and both are vastly superior to the usual regression procedures when there is moderate to high autocorrelation (i.e., interdependence). [Galton's Problem, cultural diffusion, networks, cultural evolution, statistical methodology]

1984, Sexual Division of Labor in Agriculture. Michael L. Burton; Douglas R. White American Anthropologist, New Series 86(3): 568-583. Stable URL: http://www.jstor.org/pss/678338

Abstract: Female agricultural contributions decline with agricultural intensification. We formulate and test a theory of the processes of agricultural intensification that explains a high proportion of the variance in female contributions to agriculture. Five variables show replicable effects across two or more regions of the world. These are number of dry months, importance of domesticated animals to subsistence, use of the plow, crop type, and population density. Of these, the first two are the most powerful predictors of female agricultural contributions, while population density has only very weak effects

1981. Sexual Division of Labor in African Agriculture: A Network Autocorrelation Analysis. Douglas R. White; Michael L. Burton; Malcolm M. Dow.. American Anthropologist, New Series, 83(4):.824-849.. Stable URL: http://www.jstor.org/pss/676244 NOTE: This article contains high-quality images.

Abstract:A model of causes and consequences of sexual division of labor in agriculture is tested using a sample of African societies. Crop type and the presence or absence of slavery are shown to be effective predictors of the degree of female contribution to agricultural subsistence, and the degree of polygyny is shown to be affected by female agricultural contribution and the form of residence. Autocorrelation effects are found and are shown to be a consequence of Bantu societies having higher female participation in agriculture than would otherwise be expected. This effect is an example of one of the kinds of phenomena that anthropologists have referred to as Galton's problem

1977 A Model of the Sexual Division of Labor. Michael L. Burton; Lilyan A. Brudner; Douglas R. White. American Ethnologist 4(2): 227-251. Stable URL: http://www.jstor.org/pss/643789

Abstract: Assumptions about economies of effort in performance of tasks in the same production sequence and assumptions about constraints on women's geographic mobility due to nursing and child care are used to derive hypotheses about the allocation of tasks in the sexual division of labor in preindustrial societies. The hypotheses constitute a locational model of the division of labor by sex that makes predictions in the form of entailments: for one sex, doing task X entails doing task Y. The predictions of the locational model are tested using a new procedure for statistical entailment analysis applied to a body of data on fifty tasks in the 185 societies of the standard cross-cultural sample. Assumptions about constraints of nursing and the effect of supplementary feeding of infants on women's participation in task activities are also tested and found to be supported from the evidence on this sample.

1990 A Cross-Cultural Historical Analysis of Subsistence Change. Candice Bradley; Carmella C. Moore; Michael L. Burton; Douglas R. White American Anthropologist, New Series 92(2): 447-457. Stable URL: http://www.jstor.org/pss/680155

Abstract. This paper reports on a comparative study of changes in subsistence patterns in small-scale communities resulting from contact with p"l obal economic force;. The local communities are represented by 87 Standard Cross-Cultural Sample Societies ("Standard Sample") (Murdock and White 1969) distributed across four major world geographic areas. This study describes the patterns and general characteristics of the societies on a new set of coded variables representing change processes. The variable set includes agricultural and nonagricultural intensification, the addition of new crops and animals, changes in settlement patterns and expansion, catastrophic loss, changes in trade and wage labor, and the date of ethnographic observation. The findings of the study are both methodological and substantive. The methodological results focus on sampling problems for comparative studies as well as the dates of observation set for sample societies. The substantive findings indicate that variables are regionally clustered, with two basic patterns emerging for the way subsistence systems are affected and changed in different world regions.

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1991 Centrality in valued graphs: A measure of betweenness based on network flow. Linton C. Freeman, Stephen P. Borgatti and Douglas R. White. Social Networks 13(2): 141-154 doi:10.1016/0378-8733(91)90017-N Copyright (c) 1991 Published by Elsevier Science B.V. All rights reserved.

Abstract. A new measure of centrality, CF, is introduced. It is based on the concept of network flows. While conceptually similar to Freeman's original measure, CB, the new measure differs from the original in two important ways. First, CF is defined for both valued and non-valued graphs. This makes CF applicable to a wider variety of network datasets. Second, the computation of CF is not based on geodesic paths as is CB but on all the independent paths between all pairs of points in the network.

1994 Betweenness centrality measures for directed graphs. Douglas R. White, Stephen P. Borgatti. Social Networks 16(4): 335-346. doi:10.1016/0378-8733(94)90015-9 Copyright (c) 1994 Published by Elsevier Science B.V. All rights reserved.

Abstract. This paper generalizes Freeman's geodesic centrality measures for betweenness on undirected graphs to the more general directed case. Four steps are taken. The point centrality measure is first generalized for directed graphs. Second, a unique maximally centralized graph is defined for directed graphs, holding constant the numbers of points with reciprocatable (incoming and outgoing) versus only unreciprocatable (outgoing only or incoming only) arcs, and focusing the measure on the maximally central arrangement of arcs within these constraints. Alternatively, one may simply normalize on the number of arcs. This enables the third step of defining the relative betweenness centralities of a point, independent of the number of points. This normalization step for directed centrality measures removes Gould's objection that centrality measures for directed graphs are not interpretable because they lack a standard for maximality. The relative directed centrality converges with Freeman's betweenness measure in the case of undirected graphs with no isolates. The fourth step is to define the measures of this concept of graph centralization in terms of the dominance of the most central point.

1996 Kinship networks and discrete structure theory: Applications and implications. Douglas R. White, and Paul Jorion. Special Issue on Social Network and Discrete Structure Analysis. Social Networks 18(3): 267-314. doi:10.1016/0378-8733(95)00277-4 Copyright (c) 1996 Published by Elsevier Science B.V.

Abstract. Confusions between substantive and relational concepts of kinship as a social network have led to a number of problems that are clarified by a temporally ordered relational theory of network structure. The ordered-network approach gives rise to a novel means of graphing the social field of kinship relations, while allowing kinship to be locally defined in culturally relative terms. Its utility is exemplified in applications to kinships among US Presidents, Old Testament Canaanites, and native Australians of Groote Eylandt. The formal concepts treated in the mapping of kinship networks are: kinship axioms, parental graph structure, core, circuits of consanguineally and affinally linked kin, sides and divides, homeomorphic mappings, homomorphisms as potentially simplifying mappings of kinship, elementary structure, and order-structure. Representational theorems are proven about homeomorphisms, cores and circuits, and the ambiguity of elementary structures. The last set of theorems leads to clarifying and redefining some of the basic concepts of elementary, semi-complex and complex structures of kinship in terms of properties of generationally ordered networks. The conclusions of the formal argument are 'post-structural' in the narrow sense of demonstrating the need for specifying contingent historical processes in the structural analysis of kinship as a social field. The open-ended approach to change, one that is implied by the study of ordered structures that unfold in a temporal succession, connects to issues of population variability, selection, and evolutionary processes. The kinship structures that are mapped in this approach are not intended as any sort of complete representations of kinship 'systems', but merely as scaffoldings that help to bring into view kinship as a social field, providing a baseline for other mappings (which may be superimposed) of social processes such as communicative fields, exchange processes, transmission of learned behaviors, social rights and inheritance, political and religious succession, and the like.

1971 Douglas R. White, George P. Murdock, Richard Scaglion, Natchez Class and Rank Reconsidered Ethnology 10:369- 388.

This 1971 reconstruction of how individuals were actually linked historically in the social networks of the Natchez people provides a classic example of how processual and network modeling can reveal and clarify inferences about social structure. The famous "Natchez Paradox" was discussed in virtually every introductory Anthropology text up to the publication of this article. See current accounts of the historical Natchez and the bibliography on the Natchez. Descendants of the Natchez today are recognized among the Southeastern American Indian groups and among mixed descendants of English colonists. Among these descendants, in turn, are today's recognized Natchez political leaders. Perhaps only the Encyclopedia Britannica is still remiss in describing Natchez social structure as a four-class system, as in Swanton's reconstruction of 1911. Swanton's reconstruction, however, implied a self-immolating social structure characterized by the Natchez Paradox as explicated in the abstract below. Only traces of this Paradox, compounded from several sources of ethnographic misunderstandings, are alive in urban legend and on the WWW today, such as Bennet's memory of discussions by Adam Przeworski (2004). The abstract that follows, simply because Ethnology publishes articles without abstracts, was written only in 2005.

Abstract Textual analysis, simulation, comparative distributional evidence, and prosopographic network methods are used here to solve the Natchez Paradox first posed by C. M. W. Hart in 1943, expressed in mathematical form by Samuel Goldberg in 1958 and summarized, in terms of analytical dilemmas, inconsistencies, and possible 'solutions,' by Jeffrey Brain in 1971. The Natchez Paradox emerged from an ethnographer's reconstruction of four Natchez social classes, three of which -- Sun rulers, Nobles, and Honoreds, as opposed to Commoners -- had been assumed by the historical ethnographer, John Swanton, to be ranked exogamous matri-descent groups. While all nobility married commoners, the children of males would be expected to belong to their mother's group. Swanton concluded from his reading of the contemporaneous historical texts of the 18th century French colonists that the children of men in the Sun, Noble, and Honored classes did not revert to commoner status but only to one level lower in the social hierarchy. The paradox shown by Hart and demonstrated even more strongly by Goldberg in his mathematical model is that given equal reproductive rates of marriages of different types over successive generations, combined with Swanton's hypothetical social rules, the Sun lineage would constitute a stable proportion of the population, the Noble lineages would increase their proportion in each generation, and the Honored lineages would increase proportionally to the proportion in the Noble lineages, thus obliterating the commoner class in relatively few generations.

What we find in our prosopographic counting of individuals mentioned by name in the historically contemporaneous French texts is that the only persons with Honored status who were mentioned in these texts were men, and consequently, without Honored women, there were no Honored lineages and no Honored class. The textual sources are clear that Honored status was a social rank for men, so that Honored matrilines (and their female members) were clearly an invention of Swanton, possibly because he did not base his analysis on mentions of individuals in the French texts, which are numerous, but only on presumed categories. The other probable mistake in inference derives from the fact that while French words in the singular indicate gender, the plural term 'les Honores' applies equally to men in the plural and to both genders in the plural. Swanton overgeneralized, in our view, in drawing the inference that there existed a social class of Honoreds that contained both men and women. Women with that status simply did not exist. Honored, we show, was a term only for male rank, not a designation for social class or for a set of distinct matrilineages.

The Natchez Paradox also arose from Swanton's erroneous rejection of a contemporaneous account given in one of the documents written by French colonists that delineated a consistent system of devolution of noble rank that depended on distance from the Royal line. By this firsthand account from someone conversant with the nobility, the children of Sun men (the royal lineage) devolved to Noble status for both men and women, but Noble status in the female line of descendants of these women devolved, after three generations, to Commoner status for women but for men to Honored rank. It was only the sons of men of Honored rank, in this account, who became commoners. Commoners, however, could also achieve Honored status by fame through their exploits in war. Part of the reason Swanton disputed this French account of Natchez nobility was because of the asymmetry of rank assigned to children of Noble men: even if such a man was a matrilineal greatgrandchild of a ruler, his sons were Honored while his daughters were Commoners. Such asymmetries, which Swanton mistakenly thought of as matters of asymmetric descent rather than of rank, seemed unlikely to Swanton. As described in one of Swanton's own publications, however, our distributional analysis of cases in the neighboring region identifies the neighboring Caddo as having asymmetric gender status of precisely the Natchez type. The Caddo and Natchez had long engaged in trade, so this asymmetric assignment of status need not be disregarded as a valid ethnographic feature of the Natchez status system. The Natchez paradox, then, was apparently the result of various compounded errors, including Swanton's assumptions about symmetries in rules of descent as concerns sons and daughters. Swanton did not differentiate clearly the different elements of rank, class, and lineage as they operated in Natchez society.

The simulation study uses difference equations, generation to generation, comparing demographic assumptions of earlier models aiming to "resolve" the Natchez paradox by differential reproductive rates, and the descent rules reconstructed from other evidence, in which case no further reproductive adjustmets are needed to "balance" the demographi composition of different social classes.

We regard these multiple sources of evidence as providing a definitive alternative description of Natchez social structure than that proposed by Swanton in this reconstruction of 1911, roughly 180 years after the dispersal of the Natchez as a distinct and integral society. This was a complex society with an hereditary aristocracy and complex rules for the devolution of status and rank. Swanton recognized only certain aspects of this complexity. When it came to Natchez principles of devolution of rank in the Royal and noble matrilines, many of which are common to royal lines, Swanton was unwilling to recognize the similarity to those found in other monarchical polities. The Natchez Paradox re-emerges, then, as an example of the use of network and mathematical models both as a check on ethnographic interpretations in the reading of historical texts and as pointing the way to better solutions in the rereading of textual data. Textual data can easily be misinterpreted. In the present case Swanton evidently overrelied on categorical inferences that fit his prior assumptions. Errors of this sort can easily overtake even the best of ethnographers, a category into which Swanton, in his extensive published works and his many ethnohistorical and ethnographic contributions, has long occupied a place. It is a credit to the Natchez historical corpus, on which Swanton relied, that some of his errors of inference can be corrected based on a reexamination of the textual evidence.

The appendix provides a network and genealogical analysis of the 20 prosopographic mentions of Sun royalty and how ranking within the royal lineage related to the center-periphery occupation of political posts in the Kingdom. It is also shown how the center-periphery structure of the ruling lineage exacerbated internal political divisions in the war with the French, and the exodus of one branch of the Natchez population to merge with Southeastern groups and towns such as those of the Creek, Chickasaw, and Cherokee.

For a final piece of an American Indian perspective on the Natchez Revolt leading to total destruction of Natchez society by the French see November 28, 1729.

Software Manual Publications

1994 Douglas R. White Fisher-B: A Program for an Exact Significance Test for Three-Way Interaction Effects. World Cultures 8(2):37-39.

Abstract: Fisher-B is an interactive FORTRAN program that performs two functions. First, it calculates the Fisher's exact test and gamma measure of association for 2x2 tables. Second, it tests the null hypothesis of no three-way interaction among the variables in a 2x2x2 contingency table. White et al. (1983) discuss the mathematical logic of the tests. The program can be run from within WINDOWS or from the DOS command line. Since the data are entered from the terminal, the user must prepare the contingency tables before running the program. The results are displayed on the screen and can be output as an ASCII file. A series of tables can be evaluated within a single program session. A limitation of the program is that the total number of cases cannot exceed 300.

1996. Douglas R. White and Patrick J. Gray. CORR-REL: A Program for Reliability Assessment. (html) World Cultures 9(1):7-32.

Abstract: CORR-REL is a C++ program described in White (1990) as originally programmed in Fortran. The program offers four options. First, it can read a file containing a correlation matrix and calculate reliabilities of the variables. .Second, it can read a file containing raw data and compute a correlation matrix. The third option duplicates the second, but provides estimates of reliabilities produced by three procedures. The fourth option duplicates the third and creates a composite scale using optimal single-factor weights. The program can read raw data files created by MAPTAB and SORT programs as well as ASCII files with a space between variables. Output is displayed on the screen and posted to a user-named ASCII file.

1986-1996. Douglas R. White. MAPTAB: Cross-Tabulation, Recoding, Mapping, and Data Management for the Cross Cultural Database. (html) World Cultures 1(3) Entire issue, with SCCS database. New Editions: 1986, 1987, 1988, 1989, 1993 edition, 1994.

Contents:
Preface - Stephen P. Borgatti
Installing MAPTAB 4.0 - Peter Peregrine
Tutorial for MAPTAB 4.0 - Peter Peregrine and J. Patrick Gray
MAPTAB 4.0 User's Guide - Peter Peregrine and J. Patrick Gray

1980. Douglas R. White. Regular Graph Equivalence: Algorithm for Relational Blockmodeling of Social Networks, FORTRAN program for the IBM PC. Completed under 1976-1980 NSF grant "Network Analysis of Compadrazgo and Multiple Role Systems in Rural Tlaxcala," with Lee Sailer, Research Assistant, L. Brudner and H. Nutini, co-PIs.. Web publications REGGE: Regular Graph Equivalence and REGDI: Regular Graph Equivalence.
Regge is now implemented in the original version in NetMiner (Cyram Co.). A fortran compiler may be downloaded from MinGW, a site identified by Alex Ziberna in investigating variants of the rege programs.

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YEAR AUTHOR TITLEr. JOURNAL 22:19-27.

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Unpublished Manuscripts

2005 Transforming Ethnographic Data and Analytical Problems into Network Data Suitable for Complementary Analysis and Theory Douglas R. White and Patrick Heady. Submitted to the Halle Max Planck Institute for Social Anthropology

Abstract. The paper is designed to serve as a guide for integrating network analysis into major research institutes in social anthropology and related fields.

2005 Jason Owen-Smith, Walter W. Powell, and Douglas R. White. Network Growth and Consolidation: The Effects of Cohesion and Diversity on the Biotechnology Industry Network. Submitted to Management Science, Special issue on Complex Systems Across Disciplines. Download: Growth_andConsolidation.pdf

Abstract. The growth regimes of complex networks account for many of their structural features and behavioral effects. Social and economic networks, however, tend to expand along different pathways than their technological or biological counterparts. Complex inter-organizational topologies are characterized by tight-knit clusters of prominent nodes whose dense inter-connections help forge them into an elite that can play gatekeeper and arbiter roles in an expanding network. The characteristics of such emergent elites, however, depend intimately upon the structural locations of the partners that form new ties. Systems where cores deepen their internal connections conserve their position, but may calcify. Those that expand their reach by forming connections to newcomers and to the network's periphery increase responsiveness at the possible cost of incoherence. We draw on twelve years of dynamic network data from the international biotechnology industry to demonstrate that a mix of expansive and conserving ties account for that industry's particular combination of stability and responsiveness. This structural view of network growth offers new insights into the distinctive features of social and economic networks, while linking models of network dynamics to debates in organizational theory and innovation studies.

2004 Douglas R. White and Frank Harary, Collective Geodesics and Co-evolution: A Graph Theoretic Structural Model. Submitted to Advances in Complex Systems (ACS).

Abstract. Under certain conditions, when diverse individuals (e.g., ants, individuals, agents) independently traverse a sequential decision space in reaching objectives (e.g., as modeled by a maze) they acquire synergetic properties of global problem solving (even in the absence of global knowledge about the problem space) by virtue of some form of pooling experience. The laying of pheromones on random paths taken by ants, for example, has been shown to map the set of shortest paths to a food source. This paper shows the conditions under which certain very general classes of mazes have the property of "collective advantage" to finding shortest paths by aggregating ceretain types random individual behavior (individuals have local but no global knowledge of the maze and no perception or reckoning of network distances). Of three factors considered as conditions for collective advantage, two were identified by Johnson (2000, 2001) from simulations: First is the method of traversal of the maze, and second is the method of marking trails towards a collective solution. The third - the structure of the maze - is explored here through graph theoretic concepts. These include precise definitions, theorems and observations, and simulations. They provide a language and a set of results as to the structural factors that affect collective advantage. In general, biconnected maze networks - where every node has independent paths to every other -, with many parallel paths, and many crossover paths between them, assist collective advantage. Rules developed to measure the collective advantage of a maze help to refocus the problem on the coevolution of the learning environments that endow agents with collective intelligence that is distributed across their behaviors and not condensed by selection for individual actors with better forms of global strategies or global knowledge. Results support March's (1991) findings of advantages to exploratory behaviors over selection for exploitation.

2005 Douglas R. White, Artemy Malkov, and Andrey Korotayev. The Periodic Theory of Elements for World Population Submitted to Structure and Dynamics Download: FoersterShort1.pdf

Abstract. Given that a power-law growth dynamic giving way as predicted by von Foerster et al. (1960) to a global demographic transition has been occurring since 1962, we examine the long-term time-series of conventional estimations of world population to see if one or more similar transitions occurred in the past. There is no scientific justification to reject the proposition of one or more very long earlier periods of stable quadratic growth rates that were higher than those observed for the period 1750-1958. These would have necessarily led to earlier singularities that would have produced earlier demographic transitions, like the one observed today. We reject one of the alternatives, that human evolution to date has been governed by a single trend of power-law growth that recently approached a singularity that predicts transition to slower growth. We find instead a coherent theory that connects variation in the connectivities of growing segments of the world population with (1) transition from early exponential growth, (2) quadratic growth in the early period of urban growth and associated trade and other connectivities, with a phase transition to lower growth associated with a power-law growth-reducing singularity, (3) population fluctuations after this first 'collapse' of sustained high-level growth, (4) settling in of steady lower growth rates from 1650-1962, again with a demographic phase transition to lower growth associated with a power-law growth-reducing singularity, and (5) a recent demographic transition for which the long-term trend characteristics are yet unknown, the possible trajectories of which are usefully informed by the historical record and mathematical modeling. We show that the power-law model is not simply one of estimating trends and noting changes in an ad hoc and atheoretical way. Rather, because these models imply a population dynamic close to singularity points, they constitute an explanation of phase shift that does not imply any particular set of mechanisms, only that there is a sufficiency of mechanisms, ones that may differ from region to region, to bring about phase shift prior to singularity. How this mechanism-independent explanation works is explicated.

2004 Douglas R. White Social Scaling: From scale-free to stretched exponential models for scalar stress, hierarchy, levels and units in human and technological networks and evolution. ISCOM working paper. For submission to: Computer and Mathematical Organization Theory Download: 1982scalingDRW.pdf

Abstract: Johnson's (1982) model of scalar stress deals with how networks are stacked at different levels to reduce information and energy load by substituting relationships among leaders of hierarchically ordered groups for relationships among members of larger groups at a lower level in the hierarchy. The logic and scaling results of this model are important elements in a theory of network and social scaling. They point to the possibility of scale-free modeling of the modularity of networks based on the relative constancy of the basic units at the individual level that give structure to these networks, the flexibility of how particular groups are organized, the fact that network hierarchies are population-filling with scale-free relationships to population size, and the bulking, organization and conservation of energy, information and material in ways that match the constraints on populations of individuals. These characteristics of scale-free modeling have been successful in biology, and social scaling may well follow the same principles. This article suggests the kinds of modifications that made be needed for larger-scale integrative projects in social scaling.

Hierarchical and power law models have been much debated in recent decades and their limitations exposed. While Johnson's work contains important insights, this paper examines new types of models that account for observed attenuations in the finite regimes of scale-free distributions (the stretched exponential model) and broken scale-free regimes. A combination of stretched exponentials and network modeling is found to be a productive approach to social and economic scaling that yields theoretical predictions about basal units, moments of distributions, regime attenuation and broken regimes.

Studies of scale-free, cutoff, and hierarchical properties of the U.S. airlines network in 1997 and a physics citation network are used to compare Johnson's findings with basal unit and scale-free regimes in a more general scaling model that uses the stretched exponential. This model estimates hierarchy levels and basal unit characteristics and finds a similar basal unit of 6 for renormalization at a second level (hubs for local neighborhoods) in the airline industry, suggestive of Johnson's results. The citation network suggests three-levels of multiplicative effects and a basal unit of 3 that is well under Johnson''s limit of 6 but constitutes a minimum unit of social cohesion.

New papers

2005 Douglas R. White Conceptual Ethnography: Integrating Disciplinary Practice For submission to Structure and Dynamics eJournal of Anthropological and Related Sciences, Download: CE1.pdf

Abstract: Conceptual ethnography begins from the recognition that the compartments and conceptions of anthropology and ethnography are interlinked. Here I examine cognition and social networks in relation to the concept of culture, exemplified in the study of kinship. Concepts used in network analysis of the context and behaviors involved in kinship lead to new understandings of patterns of cohesion. Within cohesive groups, people in various communities are shown to use the network itself to compute categories of kinship in unexpected ways that do not require the kinds of assumptions anthropologists often make about the connection between kinship terminology and behavior. It is shown that this lends support to the view that cognition cannot be considered an internal mental process but involves the social environment itself as part of the cognition in the wild, as Ed Hutchins has aptly put the case. Hence culture cannot be considered in terms of models of internal states, and a definition of culture must deal with the many layers of interconnections between behavior, networks, cognition, and socially cohesive units such as community or organizations in which people interact.

pub/CitySizeHierarchies.doc

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pub/ScaleableConcepts_DRW.doc

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2004 Douglas R. White and Michael Houseman, Taking Sides: From Coherent Practice to Macro Organization. Submitted to American Anthropologist.

Abstract. We show how simple rules shared by actors acting somewhat independently and with local rather than complete global information can nonetheless generate coherent global structures. In the case of dual organization, from analysis of actual marriage networks and genealogical linkages, we find many ethnographic instances where two-sided networks and marriage choices go unnoticed by ethnographers because global labels and descent rules for sides are absent. To understand global structures and institutions that may be at play, unnoticed, in social systems, it is simply not sufficient to look for shared labels attached to the parts of global structure: their structure may reside in patterns of relationships, in their instantiation. What patterns residing in relationships instantiate, however, is not necessarily a set of local decision rules that are shared and identically labeled, but rather sets of local outcomes of behavior that contribute - in possibly heterogeneous even if structurally equivalent ways - to a global configuration.

2001 Douglas R. White (UC Irvine) and Michael Houseman (Paris EPHE) Sidedness: 160 Million Strong? Abstract of presentation for the American Anthropological Association.

Abstract. We show how simple rules shared by actors acting somewhat independently and with local rather than complete global information can nonetheless generate coherent global structures. In the case of dual organization, from analysis of actual marriage networks and genealogical linkages, we find many ethnographic instances where two-sided networks and marriage choices go unnoticed by ethnographers because global labels and descent rules for sides are absent. To understand global structures and institutions that may be at play, unnoticed, in social systems, it is simply not sufficient to look for shared labels attached to the parts of global structure: their structure may reside in patterns of relationships, in their instantiation. What patterns residing in relationships instantiate, however, is not necessarily a set of local decision rules that are shared and identically labeled, but rather sets of local outcomes of behavior that contribute - in possibly heterogeneous even if structurally equivalent ways - to a global configuration.

2002. Narda Alcantara Valverde, Silvia Casasola Vargas, and Douglas R. White. The Marriage Core of the Elite Network of Colonial Guatemala.

Abstract. Following Houseman and White's definition of the core of a marriage network, we identify the core of the elite network of families colonial Guatemala in the period 1680 and 1800 in structural terms, ones related both to the concept of marriage relinking, used in research on the social organization of cognatic societies, and to the concept of wealth consolidation through structural endogamy. To test hypotheses about the relationship between the structural core of relinked marriages and the consolidation of wealth and prominence in a sample of elites in the richly documented dataset assembled by Casasola (1998, 2001), we develop a second measure of the prestige core of a marriage network, and measure the correlations between the two measures. The second measure uses the notion of network redundancy (White, 1998), in this case, redundancy between husband and wife in the accumulation of prestigious family names. This set of definitions is useful describe the structure and dynamics of cognatic descent groups, such as the Spanish kinship system. We find support for the following hypotheses:

• The meaningful family subgroups are not unilineal descent groups but sets of cognates that are more densely intermarried, through various kinds of relinking.
• Structural endogamy based on relinking is associated with wealth consolidation and thus with higher prestige.
• Structural cohesion added by sibling and sibling-in-law links reinforced by structural endogamy is associated with consolidation of wealth from different ancestral sources.
• Reconsolidation of wealth through relinking marriages is more likely the greater the number of siblings because this entails the division of family inheritance amongst a greater number of heirs. Relinking marriages will be less important when there is a single child as heir.
• The type of relinking that is most important to membership in the prestige core of the marriage network is not the marriage between blood (consanguineal) relatives, but horizontal relinking between families and sibling sets, which resemble cycles of endogamous marriage among sets of families.

2003 Douglas R. White, Emergence, transformation and decay in pastoral nomad socio-natural systems. to appear in Emergence, Transformation and Decay in Socio-Natural Systems, edited by Sander van der Leeuw, Uno Svedin, Tim Kohler, and Dwight Read.

Abstract. A network approach to economic organization, kinship systems and complexity dynamics is used to explore nomadic pastoralism as a socio-natural system. Graph theoretic measures of network cohesion are related to issues of the emergence, transformation and decay of social and economic networks and their sustainability and resilience in relation to the environment and the organization of energy, material, social, and informational flows.

2003 Andrey Korotayev and Douglas R. White, Reliability and Validity: One Factor and Third Factor Tests, Chapter 7 in Cross-Cultural Research, submitted to World Cultures.

Abstract. Third factor tests using cross-tabulation methods are at the leading edge of cross-cultural research because they get us to think about replicating results, testing validity by controlling for reliability, discovering new relationships that are the result of interactions among variables, identifying invalid relationships by controlling for third factors, and showing how certain correlations are valid withing certain contexts but not others. One-factor tests help to overcome some of the limitations of cross-cultural research by testing for reliability and developing combined measures with higher levels of reliability.

2005 Douglas R. White and Andrey Korotayev, Statistical Analysis of Cross-Tabulations, Chapter 5 in Cross-Cultural Research, in manuscript (earier version published in World Cultures.

Abstract.

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