Alcantara-Valverde, Narda. 2001 Kinship, Marriage, and Friendship Ties in the Mexican Power Elite. Investigacion doctoral. Universidad de California. Profesores Douglas R. White (UCI, Director de tesis) y Guillermo Espinosa Velasco (IIMAS-UNAM, Asesor Nacional).

Casasola Vargas, Silvia. 2001. Prominence, local power and family networks in Santiago de Guatemala: 1630 -1830. Doctoral thesis: UC Irvine.

Appelt, Cathleen Jane. 2002. "As the Den Turns: Pack Status as an Emergent Property of Interpack Mating Alliances and Occupation of Territory among Wolves in Yellowstone National Park, 1995-2000." Ph.D. Dissertation, Department of Sociology. University of Pittsburgh.

Fitzgerald, William. 2004. Structural and Non-structural Approaches to Social Class: An Empirical Investigation. PhD Dissertation, Program in Social Networks, UC Irvine. (Bevis Marks case study)

Schnegg, Michael. 2003. Das Fiesta Netzwerk: Soziale Organisation einer mexikanischen Gemeinde, 1679-2001. Ph. D Dissertation Hamburg, Department of Anthropology.

Skyhorse, Patricia. 2003. Residence on Romanum Revisited. Ph.D. Dissertation, Program in Social Networks, University of California, Irvine. Article: Adoption as a Strategy on a Chuukese Atoll 1998. The History of the Family 3(4), Special Issue: Adoption and Family Recomposition: Inventing Family Continuity. Edited by Antoinette Fauve-Chamoux.


The Marriage Strategy of the Power Network in Colonial Guatemala Silvia Casasola and Narda Alcantara-Valverde. Sunbelt Social Networks Conference 2003. Cancun.

Narda Alcantara-Valverde & Silvia Casasola Vargas. La estrategia matrimonial de la élite de Guatemala colonial. Redes Sociales, Teoría y Aplicaciones. Gil-Mendieta, Jorge & Samuel Schmidt eds. México: Universidad Nacional Autónoma de México, 2002, pp.157-178.

Douglas R. White

Introduction: White et al. (1998-in press, Brudner and White 1997) develop a theory of a particular form of social integration based on multiple connectivity, in which every pair of nodes is connected ("relinked") by multiple independent paths. Elaborating one of the dominant hypotheses in the theory of social class, for example, they argue that multiple connectivity of marriage links between families defines a boundary condition for cohesive social classes. They apply this theory, which recognizes a generalized and potentially large-scale networked basis for cohesive social integration, to explain the basis in network evolution of two different systems of social class. There is a critical density threshold for the transition to a giant multiple-connectivity core of a network, and the kinship network in the two cases studied have passed this threshold. After a network has evolved in density beyond the criticality transition, its nodes partition into a giant core in which every pair of nodes is connected by multiple independent paths; a periphery of nodes connected to the core by a single path, and marginals not connected to the core. In the Tlaxcalan case the principle of equal division of inheritance assimilates part of the periphery - the descendants of the core - into the same class as the core. This contrasts with their study of an Austrian village with an unequal division of inheritance between principal heirs of estates and children who are bypassed as principal heirs, where the class division is more strictly between core and periphery-plus-margins.

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.

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.

[[The following two articles represent a second theoretical application of the related concepts of structural endogamy and multiple connectivity as identifying an empirical variable or boundary condition within social networks that is linked in causal-explanatory ways to social class formation. Here, ranked statuses differentiated by wealth are integrated into a single solidary social class by ties of marriage and compadrazgo that avoid homogeneity of rank and actively cross-cut rank differences with greater than random frequency. As hypothesized from a structural endogamy model, structural endogamy integrates a core of 38% of the couples in community to which up to nearly 90% of the entire community are connected by marriage, if not by marital relinking. Unlike the Austrian case, however, those who are not relinked are not descendants of core property- owning ancestors, but rather are immigrants from other villages or the descendants of unrelinked immigrants. Relational analysis shows that the children of core couples may marry outsiders but resist intermarriages with descendants of outsiders that would lead to bringing peripheral lines of outsiders into relationships of relinking or structural endogamy. Moreover, nearly 100% of the structural endogamy is within the village. Eventually, however, as the descendants of outsiders persist in living in the village for several generations, they are gradually absorbed into the relinked core. This fits the predicted model of a one-class social system, but with local solidarity and the gradual absorption of outsiders, or a local core-periphery structure. Further, it is shown that the great majority and most important types of compadrazgo ties are oriented not towards the periphery of the village but towards other neighboring villages, integrating the cores of different villages into a single class system. Relinking also occurs between villages but only for compadrazgo ties.]]

Abstract. This paper develops a concept of social integration based on multiple pathways of connectivity. In a cohesive set of a network, every pair of nodes is connected by multiple independent paths. This measure of cohesion identifies maximal group boundaries independent of density or proximity. It is ideal for the study of cohesion on a large scale. In a network study of the two most important social relations in a Mexican community - kinship and compadrazgo (ritual kinship) -, we confirm theoretical predictions as to effects of social cohesion, such as higher participation in local offices by members of cohesive sets. Both kinship and compadrazgo have passed a critical density threshold in the ratio of network edges to nodes for transition to a network in which the nodes are partitioned into the structural positions of a giant core in which every pair of nodes is connected by multiple independent paths, a periphery of nodes connected to the core by a single path, and marginals not connected to the core. The dimensions of our analysis include the relative density of the independent social relations, the structural positions they define, the relative spatial extensions of their cores, the manner in which these cores cross-cut one another over time (such as the local concentration of the sparser kinship core versus the quicker-to-relink extensions of the compadrazgo core), and the question of how migrants are absorbed from one spatial location to another over time. How separate networks and their institutional forms interrelate on these dimensions give new insights on the dynamics of social cohesion, social class, and large-scale "invisible communities" that relink families within and between the local segments of a regional social system. The present case is one of extended group cohesion associated with egalitarian norms and informally organized resistance to power groups from outside.

This article presents a new way to conceptualize social integration based on different modes of connectivity in network components. Within a social network, a multiply connected component is one where every pair of its nodes is connected ("relinked") by multiple independent paths. Social boundaries are derived from multiple connectivity as follows: For any network, there exists a critical density threshold for the transition to a giant multiply connected core. After a network evolves in density beyond the criticality transition, its nodes partition into (1) a giant core in which every pair of nodes is connected by multiple independent paths, (2) a periphery of nodes connected to the core by a single path, and (3) marginals unconnected to the core.

We test three facets of a theory of integration by differential modes of connectivity as it applies to a study of the social networks of a Mexican village. First, we show that the set of boundaries of social groups defined by differential connectivity are correlated in turn with predicted features of social cohesion, such as social participation in the central community institutions. This provides construct validation for the theory and predictions from network structure to emergent social phenomena.

Second, we apply our theory of a generalized and potentially large-scale networked basis for cohesive social integration to explain certain aspects of the network evolution of different systems of social class. Elaborating one of the dominant hypotheses in the theory of social class, we argue and demonstrate that multiple connectivity of links between families defines a boundary condition for cohesive social classes. Social network findings are matched by belief statements of villagers regarding egalitarian social relations among members of Tlaxcalan heartland villages. This provides construct validation for this application of the theory to the present case, where the principle of equal division of inheritance assimilates part of the periphery - the descendants of the core - into the same social class as the core, although the mode of connectivity is weaker.

Third, we apply our theory of cohesion to the differential structures and functions of two social relations that are fundamental to Mexican social organization, examining how multiple connectivity operates first for kinship networks, then for compadrazgo (ritual kinship between parents and godparents), and finally, for both in combination. In the kinship and marriage network, relinking is only locally cohesive as it occurs only within the village. In the compadrazgo network, in contrast, multiple connectivity integrates the village with other villages in the locality into a large-scale local segment of an "invisible community" of the regional egalitarian social class system, in which inter-village migration is facilitated. Combining both social relations under one framework reveals an astonishing synergetic effects both for village and regional integration. On the dyadic and on the broader structural level both networks are almost orthogonal to one another and thereby perfectly complement one another. Compadrazgo simply cross-cuts the limitation of the kinship and marriage network and knits new migrants and other more loosely connected families into the community long before the marriages of their children could do so in further generations.

Abstract and Review: "Methods and techniques [of kinship analysis] have strong implications on the theoretical side. For that reason, their use pertains to the reexamination of kinship nomenclatures. [In the Godelier et al., edited volume, 1998] One article vigorously distinguishes itself in the domain of precise procedures. In contrast with Tjon Sie Fat, who presents a meticulous algebraic treatment of purely terminological kinship, Michael Houseman and Douglas R. White, using a variety of computer tools, collaborate to show the emergent properties of a network of marriages that are effective through their dynamic aspect in the pratique -- behavioral practices -- of matrimonial alliances, where they find observed regularities that are not a simple effect of a terminological logic and rules of marriage. These constitute, at the level of practice, a sort of primary behavioral regularity [encodage], of a complex order. This is precisely demonstrated in that the two researchers, in the course of their analysis, are able to detect a structure of sidedness [structure à coté], or bipartite network where a pair of supersets of marriages, connected by agnatic and uterine decent links, operate so as to organize network configurations of marriage alliances across a range of societies in lowland Amazonia. The authors succeed in creating an empirical sociology of high quality that takes the first steps towards a conceptual and theoretical advance towards a sort of grounded theory (Glaser and Strauss 1967) based on facts established methodologically through carefully controlled working hypotheses [and precise analytic definitions]" (translation from review by Jean-Luc Jamard in L'Homme 2000:735-736).

The p-graph approach that has proven an invaluable aid to the study of kinship, marriage and genealogical network analysis here is explicated - 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.

In writing an introduction to this refereed book, in which two articles of the co-editor appeared, we argue for a paradigm that treats social action such as kinship and exchange and decision making as embedded in a specific nexus of social relations that require a dynamic approach to social transactions, taking into account the local variability of resources and of positions within the network of relations, and giving an account of how the actor as agent is both embedded in and productive of choices and links that will perpetuate or dynamically alter social structure and organization. We argue for a network-based reconfiguration of theories of social exchange, the distribution of personal rights, and the biography of material and symbolic goods as they flow through temporal networks intersecting with the biographies of individuals and groups.

This ethnographic and historical study of social networks in Tlaxcala, Mexico, examines a number of hypotheses derived from the idea that the number of independent paths connecting individuals is a source of social cohesion with measurable consequences. "Biconnectivity" is where all individuals in a group have two or more independent paths of connection, and "higher order connectivity" applies where there are more than two such paths. The general hypotheses are:
(a) Biconnectivity is a source of emergent, potentially decentralized social cohesion that can occur (with observable effects) at low density in the bicomponents of relatively stable social networks.
(b) This is especially true for relations that have very high "currency" or life-support salience, such as relations of political influence, property transmission, or kinship and marriage connections.
(c) Hence, social class, elites, wealth-transmission, and marriage systems are especially well-suited for analysis. Here are some further points of clarification for these hypotheses:

(d) Dynamic evolution of 1-connectivity and biconnectivity (and higher order connectivities having both global "giant component" effects and localized interaction effects) can give rise to phase transitions in network configurations that may account for observed changes in social organization and institutions.

1998 Douglas R. White and Thomas Schweizer, " Kinship, Property and Stratification in Rural Java: A Network Analysis," pp. 36-58. in Kinship, Networks, and Exchange, eds. Thomas Schweizer and Douglas R. White. Cambridge University Press.

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

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 materialproblems 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.