Abstracts 1997-2000 Douglas R. White

METHODOLOGICAL FOUNDATIONS

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.

Abstract: A network is robust to the extent that it is not vulnerable to disconnection by removal of nodes. The minimum number of nodes that can be removed to disconnect a graph is its connectivity (minimum cutsets). By Menger's theorem, the connectivity k of a graph is also the minimum of the maximum number of node-independent paths between every pair of nodes. Connectivity is proposed as well as a measure of the cohesion of a network.

We present a tuneable algorithm for computing a lower bound on the number K(i,j) of node-independent paths between every pair of nodes in a directed or undirected graph G. A variant of the procedure computes all the k-components of a graph. While an exact algorithm is NP complete, the approximation algorithm is accurate up to 99.5% for random graphs and in the several empirical networks examined was found to be 100% accurate. Exact algorithms for the k-components of a graph are also NP complete, while the approximation algorithm is subquadratic, hence applicable to large networks. In the examples we evaluate the utility of a measure of node-independent paths for analysis of robustness and cohesion.

Each node in a graph has a value Ki for the maximum connectivity of a subgraph of which it is a member. The minimum of Ki and Kj for a pair of nodes cannot surpass the value of Kij. Hence Kij gives additional information about robustness, vulnerability or cohesion relative to pairs of nodes in a network. Successively higher values of Kij are hierarchically embedded according to subgroup connectivities, but that in addition, values of Kij that are higher than their maximum subgroup connectivities represent robustness through ties inside or outside a connectivity subgroup, and hence provide additional information about network structure that is relevant to robustness, cohesion, and ties that crosscut cohesive subgroups.

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

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

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.

A co-authored methodological guide to software written by the first author assesses the classical problems 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.

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.

A co-authored methodological guide and manual describes a suite of computer programs written by the first author and included on the CD- ROM. By converting the data to a new set of graph-theoretic conventions that lend themselves to the structural and network analysis of marriage systems -- in the context of the full range of cultural diversity of systems of inheritance, descent, and social class formation – is allows the analysis of community-level or large scale genealogical databases. One program (ego2cpl) does data conversion to p-graphs representing individuals as edges connecting their family of origin to their family of marriage or procreation. Another (par-calc) computes the frequencies of different types of marriage and interfamily relinking against a new baseline for marriage-rule research (relatives of a given type married versus actually available for marriage). A third program (par-bloc) analyzes social groups and boundaries defined by patterns of relinking (connectivity by multiple independent paths) among families. A fourth program (pgraph) compares an empirical kinship and marriage network to a simulated "random marriage" baseline by permuting actual spouses taken among those available in each generation. This program also analyzes global structural characteristics of genealogical networks to assess hypotheses of dual organization, circular patterns of marriage among lineages, and others. The fourth program presents visual displays of complex genealogical networks that result from emphasizing different structural principles and provides the user with editing tools for the visual presentation of both small and large-scale kinship and marriage networks.

A new set of concepts is developed the structural analysis of kinship and marriage systems, foremost among which is that of structural endogamy, which is defined by a maximal boundary condition for groups in which all couples are connected by multiple paths of parent/child links. This concept is shown to differ fundamentally from the usual categorical definition of endogamy, which is a measure of the extent to which marriage takes place within a group defined by extrinsic criteria (territory, community, ethnicity, class, occupation, etc.). Intrinsic or relational criteria such as marital relinking among sets of families define structural endogamy in terms of emergent groups with clear-cut boundaries, and define new sets of structural variables for the analysis of social system. The concept of bounded sets of relinked marriages corresponds precisely to one of the fundamental graph- theoretic concepts, that of blocks of nodes that are 2-connected in that every pair of nodes is connected by two or more independent paths. Various kinds of 2-connected subgroups are defined for p-graph representations of marriage and kinship networks, and implications are drawn for anthropological research on social organization and modeling systems of marriage alliance. The p-graph is proven to be a foundational representation for such research.

This web site documents research material and problems from the longitudinal field site of the capital of the Tarasco in Mexico that run from 1780 to 2000 in archival form and from 1945-60-70-80-90-2000 in terms of data from ethnographic censuses. The network data from this site are currently being analyzed under a grant from the Mellon Foundation. This site provides an inventory of resources for anthropological research. This site provides an on-line inventory of publications and data sets from the electric journal founded by Douglas White in 1985 and currently available on CD ROM.