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Structurally cohesive subgroups are a powerful and mathematically rigorous way to characterize network robustness. Their strength lies in the ability to detect strong connections among vertices that not only have no neighbors in common, but that may be distantly separated in the graph. Unfortunately, identifying cohesive subgroups is a computationally intensive problem, which has limited empirical assessments of cohesion to relatively small graphs of at most a few thousand vertices. We describe here an approach that exploits the properties of cliques, k-cores and vertex separators to iteratively reduce the complexity of the graph to the point where standard algorithms can be used to complete the analysis. As a proof of principle, we apply our method to the cohesion analysis of a 29,462-vertex biconnected component extracted from a 128,151-vertex co-authorship data set.

Today a convergence between the fields of anthropology and economics has re-emerged after decades during which the dictates of methodological individualism, as strikingly elucidated by Kenneth Arrow, had seriously limited and hampered effective scholarship in studies of economic and social development in developing countries. A new generation of development economists represented by Spolaori and Wacziarg (2013) and (Spolaori 2016) has reopened the possibility of fruitful cross-disciplinary interaction, enabling economists and anthropologists to investigate those many social structures wherein resources are jointly held and wherein social goals are the product of interests held by groups, rather than exclusively by pairs of individuals stripped of a context of ethics.The continually expanding data of Standard Cross-Cultural Sample (Murdock and White 1969) provide a wide range of variables that make it possible to test theories regarding development and causality in human societies. Furthermore, new software facilitates the testing of these theories in the context of diffusion, historical language families and ecological contexts. Together, the data and the new software are essential to any effort to test theories of human evolutionary history and development.

The three sections of this article illustrate why cross-cultural research has not worked for some key social science questions and has worked for others.  The three sections involve interpretation of causality from correlations, causality not based on correlations, and maps pertinent to understanding aspects of male-female and husband-wife equalities and inequalities.

One of the universal features of human sociality is the fact that our social networks are highly integrated – human societies exhibit several nested social layers including families, bands and communities. Several factors have been identified as creating disincentives for hostile intergroup relations, including economic interdependence (trade), intermarriage (exogamy), cooperative defence against external adversaries (warfare), and lack of patrilocal residential groups (absence of patrilocality with external war). We provide a preliminary test of hypotheses relating to the correlates of amicable relations between communities (i.e. absence of internal war) using the standard cross-cultural sample (SCCS) database. Intermarriage did not have any explanatory power, there is a nearly significant effect of trade on the establishment of intergroup tolerance, and the evidential basis for cooperative defence and patrilocal residence are strong when combed into a multiplicative effect. This analysis is complemented with an exploration of the evolutionary factors underlying elementary forms of meta-group organization in non-human primates.

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.

The feature of Dravidian kinship terminology is typically that male lines on ego’s “side” marry and call their “affines” relatives in a set of opposing male lines. The egocentric versus sociocentric debate in Anthropology over the social network implications of Dravidian terminology is resolved with proof of a single theorem: For a connected network A of marriages between consanguineals, including only the additional ancestral relatives leading back to the consanguineal ancestors of those couples, then if the kin of the couples are consistently sided egocentrically, according to Dravidian kinship terminology, then all relatives in network A are consistently sided sociocentrically, whether sides are defined through opposing sides V of male kin, U of female kin, or both. Two other theorems prove that if all the consanguineal marriages in network A are same generation (same number of generations back to the common ancestor for the husband as for the wife) then if sidedness is V it is also U, if U it is also V. Finally if network A is both U and V then all of its marriages are same generation and the marriage structure of A is one of implicit alternate-generational moieties, as in a Kariera kinship network.

BdA’s model does a service by clarifying the precise structure of Trautmann’s paradigm of Dravidian South Asian (DSA) kin term structure (KTS) as rewrite rules: expressions in an algebra of Dravidian KTS that can be only shortened by rewrite rules. It imposes a “Dravidian cross-cousin marriage rule” expounded at great effort by Trautmann: “I do not hesitate to reconstruct for the Proto-Dravidian kinship system not only a terminology but a rule of social organization” contra “Sheffler’s [ineffectual] counterargument that the rule and the semantic contrast are not invariable concomitants of one another …. The question is no longer whether a cross-cousin marriage rule is ancestrally Dravidian, but what precise form that ancestral rule took” (Trautmann 1981:235-236). I will refer to BdA’s model as “the Trautmann algebra” (Tjon Sie Fat and Trautmann, 1998), so as to expose its weaknesses independently of BdA’s model since I would expect that after reviewing the commentaries BdA would modify his current model into a paradigmatic form that accords historically and ethnographically with Dravidian terminological variants. There is no loss here in the value of Trautmann’s groundbreaking work, but a significant gain in improving the quality of his model of Dravidian KTS.

The original pinpointing sheets, 2/3rds prepared by Murdock and 1/3rd by White, are printed here in the same font as they were originally typescript, with only minor spelling corrections. Only the first 113 pinpointing sheets were published in 1988 (World Cultures 4#4).

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.

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.

The Standard Cross-Cultural Sample contains the best-described society in each of 186 cultural provinces of the world, chosen so that cultural independence of each unit in terms of historical origin and cultural diffusion could be considered maximal with respect to the others societies in the sample. Often the time period chosen is that of the earliest high quality ethnographic description. Hence the SCCS is primarily a sample of preindustrial societies.The original paper, published in the journal Ethnology in 1969, presented the first research results of the Cross-Cultural Cumulative Coding Center (CCCCC), a unit established in 1968 by Murdock and White at the University of Pittsburgh, with support from the National Science Foundation. The center was organized to offer to scholars a representative sample of the world's known and well described cultures, each "pinpointed" to the smallest identifiable subgroup of the society in question at a specific point in time, and to provide the first set of coded data for the sample. The sample selected by Murdock and White has the advantages of providing a sample size sufficiently large to test multivariate hypotheses but sufficiently small to allow complete coding by different authors; one with pinpointing of dates and focal groups and with a rich ethnographic bibliography and multiple data quality ratings that facilitate cumulative coding of comparative data on a wide variety of topics.Although the SCCS maximizes the relative independence of sample cases, the 1969 article also provides standard Galton's problem controls for historical nonindependence of cases, and demonstrates with illustrations of their use that Galton’s problem controls are needed to make valid statistical inferences even with a relatively large cross-cultural sample. This cautionary scientific result has not been properly emphasized by the Human Relations Area Files, with which the SCCS has no connection other than the fact that for some SCCS societies, but not all, there exist partial ethnographic materials housed by HRAF.The SCCS has served as a basis for a cumulative series of data coded by diverse authors in hundreds of publications on many different types of societal characteristics. Cumulative ethnographic codes and codebooks are published in the World Cultures electronic journal, which adds the geographical coordinates and computerizing mapping through SPSS and the journal's MAPTAB program, written by Douglas R. White. The SCCS and its SPSS database and codebooks currently contain more than 2,000 variables contributed by nearly a hundred different studies and as many authors. These variables include those of Murdock’s Ethnographic Atlas in a form most useful for testing hypotheses because they are collated with the standard sample societies.This paper is reprinted in modified form with permission of the journal editorial office as published in Ethnology 8:329-369.

In inaugurating the Structure and Dynamics journal, we offer a conduit for refereed electronic publication, debate, and editorial communication in the domain of anthropology and human sciences. We as editors dedicate our effort to facilitating and disseminating interdisciplinary discussion and research in anthropology and related sciences. We invite you—as a subscribed reader at no cost—to contribute and to participate in raising the aspirations of the human sciences today.

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.

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.

A field experiment conducted in Central Australia in 1971–1972 explored differences between what Aborigines actually did andw hat 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 article focuses on discrepancies between expected and observed with regard to descent, marriage, and kinship. First, it examines field methods and the dataset, then reviews analytical methods used to interpret the data. The alternative analytical methods serve to test “competing hypotheses” about the nature and operation of Alyawarra descent, marriage, and kinship. 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 data continue to repay increasingly sophisticated analyses thirty years after they were recorded, thus attesting to the success of the field experiment. © 2005, Sage Publications. All rights reserved.

A recursive analysis of network and institutional evolution is offered to account for the decentralized structure of the commercial field of the life sciences. Four alternative logics of attachment - accumulative advantage, homophily, follow-the-trend, and multiconnectivity-are tested to explain the structure and dynamics of interorganizational collaboration in biotechnology. Using multiple novel methods, the authors demonstrate how different rules for affiliation shape network evolution. Commercialization strategies pursued by early corporate entrants are supplanted by universities, research institutes, venture capital, and small firms. As organizations increase their collaborative activities and diversify their ties to others, cohesive subnetworks form, 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 differential connections to diverse partners. © 2005 by The University of Chicago. All rights reserved.

The Structure and Dynamics eJournal offers a conduit for refereed electronic publication, debate, and editorial communication in the domain of anthropology and human sciences. We invite you—as an open access reader at no cost, an author at no cost, or a volunteer, to submit book reviews or commentary—to contribute and to participate in raising the aspirations of the human sciences today. To submit an article, follow the link to “Submission guidelines.” To submit a review simply click Submit a “Reader's Comment” at the article site.We comment here on the contents and success of the first two issues. Full-text downloads of the eJournal articles numbered 5,313 in the 11 months since September 23, 2005, now averaging 16-17 a day. This reflects positively on quality of the articles, made possible in turn by the high quality and incisiveness of reviews, the number and diversity of reviewers who have responded, and selection for quality in article acceptance and reviewers (and we thank our reviewers for their efforts at timely review).In just two issues, the eJournal has come a long way in attaining the goals set out for it as a publication in which scholarship and debate can be engaged in contemporary fields of research, one that provides a venue for the study of the complex interplay between dynamics and structure, and gives an outlet for methods and results which speak to the issues of simplicity in complexity and the study of structure and dynamics. It has also facilitated presentations of new forms of analysis and visualization, new forums for debate and new vehicles for the dissemination and absorption of work at the cutting edges of the human sciences.Authors of issue 1#1 have had feedback and good reception. Peter Turchin’s findings on historical dynamics have been replicated, for example, using data covering a 700-year period from archaeological research in the Southwest. The replication study is in press in the journal Complexity. Wikipedia, at http://en.wikipedia.org/wiki/Social_cycle_theory, cites Turchin’s article in issue 1#1. Several of the issue 1#1 articles are now reviewed in blogs and on-line commentaries, digests, or reference lists, many with timely google citations. Links to them are starting to appear on educational sites at which students have direct access to download and on-line readership. Issue 1#1 marked our first use of high-quality color imagery and live url links. Krempel and Schnegg’s paper explained our journal’s dynamic-gif logo in their “About the Image: Diffusion Dynamics in an Historical Network,” which also allows the reader to link to the authors’ longer 1998 study and its on-line imagery. That article, “Exposure, Networks and Mobilization: The Petition Movement during the 1848/49 Revolution in a German Town,” published at http://www.mpi-fg-koeln.mpg.de/~lk/netvis/exposure, provides further background and examples for the innovative use of dynamic graphics.Summing up our current issue, 1#2, and to give readers an idea of the unusual and unique features of electronic publication, we review the advantages and evolution of our permanent, paper-quality, refereed eJournal publications. Along with our use of live url links and imagery on-line, these advantages are facilitated by our UC eScholarship publisher.In 1#2, Sean Downey provides a fascinating study that interrogates ethnographic and historical texts with the aid of simulation. He uses his approach to analyze the ethnographic/historical theory put forward by noted author Paul Willis in Learning to Labor, secondarily to show strengths and weaknesses of contemporary social theories such as those of Tony Giddens (1984) and, finally, also to identify the descriptive lacunae that limit this genre of simulation. As an invaluable gift to students and instructors (he is himself a graduate student), he supplies on-line the code for the simulation and, as a free resource, access to the simulation software package itself.Christiansen and Altaweel’s “Understanding Ancient Societies,” subtitled “A New Approach Using Agent-Based Holistic Modeling,” describes their Argonne National Labs holistic agent-based simulation framework that couples with incredible depth to the real-world information that can be brought into simulation and modeling from the earth sciences, satellite imagery, climate modeling, the agricultural sciences, ethnography, network analysis, and a host of other areas. Focusing on the development of their model for addressing research questions about Mesopotamia, they explain and illustrate the general-purpose simulation framework. Their work offers a productive complementarity to Algaze’s lead article in our first issue, where he poses a series of questions, hypotheses, and possible lines of evidence with which to explore the processes that lead to the first cities’ takeoff.Wouter de Nooy’s study of the networks and the structural dynamics of folktale plots, tested as well against literary interactions through time among Dutch literary critics, uses network analysis software described in his coauthored book with the software authors (de Nooy, Batagelj, and Mrvar 2005). He gives us the first-ever published SVG image produced by Pajek network software with interactivity within the SVG image itself (now available from the Pajek freeware authors at http://vlado.fmf.uni-lj.si/pub/networks/pajek/). The SVG image is not simply static but directly accessible, thanks to live links inside our eScholarship pdfs, as an interactive graphic that the reader can explore for different views of the data.Wilkinson and Tsirel evaluate limit cycles in Indic regional political polarities—how many polities in each ten year interval, coded from a comprehensive database—over two millennia. They begin with the simplest of models of temporal dynamics and historical limit cycles and proceed to evaluate at each step those of increasing complexity. The visual scanability of their multicolor graphical results helps to give the reader an ability to judge visually the contribution of different kinds of statistical analyses to understanding the complexity of the data and, in turn, the plausibility of different historical processes and explanations.Seary, Richards, McKeown-Eyssen, and Baines, in their “Networks of Symptoms and Exposures,” provide an innovation that makes possible a better comprehension of statistical interactions in complex phenomena by enabling the reader to recognize linkages within complex data such as those in the field of medicine. The visual imagery of their 3-dimensional interactive “panigram” images, named from the Greek panis (“sail”), provides a generalization of simpler histograms that, by analogy, would be composed by an ordering of the one-dimensional heights of the ship’s masts. The 3-D panigrams form an analog of planar sails rotatable about masts that represent the spines of the data structure. Co-authoring with professionals in the medical field, they use these images to look at the interrelations of people, their exposures to disease, and how symptoms are jointly distributed across both.Berkowitz, with his collaborators Woodward and Woodward, draws on his scholarship about the role of family and informal institutions in historical world economies to write of venerable and legal networks of exchange that have operated for millennia and yet that make it impossible to trace financial transactions through the modern computerized credit banking systems. His scholarship, interrupted by untimely death in 2003, is honored in this issue.Palmer, Steadman, and Coe, in “More Kin: An Effect of the Tradition of Marriage,” utilize genealogical graphics, a mathematical model of networks and demography, and analysis of the relation between biology and culture to reopen important questions about the role of human kinship systems in human evolution, considered both in terms of networks and cognition. Their results for numbers of kin at various distances in bilateral kinship networks, depending both on demography and issues of social recognition, are cited in the article by Moody.James Moody’s “Fighting a Hydra: A Note on the Network Embeddedness of the War on Terror,” shares in common with Berkowitz et al.’s article a concern for misunderstandings that prompted and have emerged out of the War on Terror. Moody writes of the effects of misguided policies, such as described in the recent best seller by Thomas Ricks (2006), that fail to take into account the “blowback” consequences of the killing, wounding, and arresting of civilians and the torture of suspected insurgents. He considers as well the effects of the wounding and deaths of soldiers, recruited into such wars, on those in their home communities, families and social networks. His on-line innovation is to provide students and the reader with a calculator for the network scale-up model of Killworth et al. (1998) to estimate the number of people who know somebody in an “event,” such as those killed in the war. “Since the values needed to make these estimates are rapidly changing and somewhat subjective, users can test the effect of different assumptions with this calculator,” as noted within the calculator itself. In our review, we highlight the general properties of the scale-up model, of which we shall see more in future articles.

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.

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. © 2004 Taylor and Francis.

Five key problems of kinship networks are boundedness, cohesion, size and cohesive relinking, types of relations and relinking, and groups or roles. Approaches to solving these problems include formats available for electronic storage of genealogical data and representations of genealogies using graphs. P-graphs represent couples and uncoupled children as vertices, whereas parent-child links are the arcs connecting nodes both within and between different nuclear families. Using results from graph theory, P-graphs are shown to lend themselves to solutions of the problems discussed. Relinking of families through marriage, for example, can be formally defined as sets of bounded groups that are the cohesive cores of kinship networks, with nodes at various distances from such cores. The structure of such cores yields an analytic decomposition of kinship networks and constituent group and role relationships. The Pgraph and Pajek programs for large network analysis help both to represent kinship networks and their patterns and to solve problems of analysis.

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.

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.

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. © 1994.

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. © 1991.