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 ënavigability of strong tiesí 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 last article in the context of the full volume

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.

2003 Douglas R. White, 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

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.

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.

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. 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.

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. Behavior Science Research 12:1-249. 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.

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

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.

1974 Douglas R. White Mathematical Anthropology. Reprinted from J.J. Honigmann, ed., Handbook of Social and Cultural Anthropology:69-446

Abstract. under development

1983 Douglas R. White and Karl P. Reitz, 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.

2000 Douglas R. White and Karl P. Reitz, Homomorphismos de grafos y semigrupos sobre redes de relaciones. Política 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.

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.

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 Lilyan A. Brudner and Douglas R. White. Class, Property and Structural Endogamy: Visualizing Networked Histories Theory and Society 25:161-208.

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.

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

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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

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.

Using Galois Lattices to Represent Network Data Linton C. Freeman, Douglas R. White Sociological Methodology, Vol. 23. (1993), pp. 127-146. jstor
pw/Galois.pdf

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 © 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 © 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 © 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.

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.