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.





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

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

  [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.

  

  2007 Douglas R. White, Standard Cross-Cultural Sample draft 1.1 International Encyclopedia of the Social Sciences, 2nd edition. New York: Macmillan Reference USA

  Abstract. 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

  1990 Douglas R. White, Reliability in Comparative and Ethnographic Observations: The Example of High Inference Father-Child Interaction Measures, Journal of 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 Patrick Gray, Corr-Rel: A Program for Reliability Assessment. World Cultures 9(1): 58- 75.

  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 LÈvi-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 of entailment analysis has led us to formulate a new and power ful theory of the sexual division of labor.

  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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  MATHEMATICAL ANTHROPOLOGY

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

  Abstract. under development

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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 pdf

  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. 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 26:161-208. (the repeated footnote number, 8, on p 164 should be 9). Reprinted at eScholarship
  Available at a library near you

  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