Second, because female age at marriage is significantly lower than that of males, the axiom of generational closure - successive sibling-in-law links that close into cycles - does not apply. The age bias yields Logic2 in which recurrent patterns of marriage between patrilineages are highly asymmetric, like classificatory MMBDD marriage, rather than symmetric, as in sister exchange. Marriage practices associated with Logic2 lie within the 'norms' of Logic1, although the conventional 'genealogical' diagram for Aranda-Alyawarra type of kinship terms created by Radclifffe-Brown (1930) shows equivalence classes in which sister exchanges and bilateral second cousin marriages are permitted. His model of the Aranda "system" is one of delayed direct exchange between classificatory patrilines, following the erroneous logic of his diagram. In fact, neither sister exchange nor bilateral second cousin marriages occur among the Aranda or Alyawarra. To remedy this defect - a problem in interpreting equivalence classes in classificatory kinship terminologies - of the conventional Radclifffe-Brown model of Aranda-type section systems, the two previous proposals made by Denham et al. (1979) included an 'open format' model of directed wife-giving relationship in which women's generational time runs 50% faster than that of men. This is the model that that we call Logic2. Secondly, they created a closed double helix version of these same equivalence classes in spiraling generations that close back on themselves (we call this a helical Logic2), cyclically. They found that the open format model and double helix variant could account for both the 'normative' Aranda-Alyawarra kinship terms and the stated preferences in both cases for MMBDD marriage. What they could not explain, however, was why so very many classificatory kinship terms of the Alyawarra (23%) were non-reciprocal and why Omaha terms were often employed as an exceptional pattern outside the 'normative' pattern of kin-term usage.
In this study we use network analysis - and methods for the empirical study of equivalence classes with respect to actual behavioral patterns - to help resolve the problems still unsolved with the double helix model. A network analysis of equivalence sets, conforming to the fact that members of local patrilineages are observed to forget the matrilineal ties of departed ancestors, establishes that Logic2 is one of generations that have time intervals of different length for men and women, and are shallow, open-ended, flexible, and extensible so as to include alliances with neighboring groups. We argue that since patterns of marriage among cohorts that have departed are successively erased, these patterns fail to constrain the emergence of new patterns in cohorts where marriages are taking place more than four generations later. Thus the network pattern does not form a structure that closed on itself with a fixed algebraic kinship structure, like the double helix model, but is a limited and partial realization of that model. This finding is consistent with a dynamic of alternative marriage choices that, as their network locations and frequencies change within the possibilities offered by Logics 1 and 2, alter the very topology of the kinship and marriage network. Wife-giving and wife-taking choices of members of the named patrilineages may be realized as exceptional marriages that inflect behaviors generated by Logic2 into new systemic patterns that lead to lineage remapping of generations. This allows the kinship pattern to evolve dynamically across a class of network models (Tjon Sie Fat 1983) influenced stochastically by age distributions at marriage. This opens up the possibility of a new understanding of the evolution of social organization in Australian societies, where age differences between spouses, and classificatory terminologies consist with section systems, are very common.
The unintended effect of the demography of H>W age differences resulting from a preference dynamic is supplemented by Logic3, the widespread and intended use of an extra-'normative' Omaha terminology. A detailed analysis shows this usage to correspond to an exclusionary device that says "don't marry here," but does so nonreciprocally.
Examining relationships amongst the Logics 13 at the level of practice shows how they form a coherent dynamical system oriented towards demographically and strategically inflected adaptation. A strictly 'normative' approach to modeling Alyawarra kinship would be misleading as a theoretical paradigm. We argue for a broader framework that takes into account the interplay of multiple cultural logics as integral within a networked system of kinship practices.
2001. Douglas R. White (UC Irvine) and Michael Houseman (Paris EPHE) "Sidedness: 160 Million Strong? Abstract of presentation for the American Anthropological Association.
Introduction: White et al. (1998-in press, Brudner and White 1997) develop a theory of a very general 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.
1997 Lilyan A. Brudner and Douglas R. White. Class, Property and Structural Endogamy: Visualizing Networked Histories Theory and Society 25:161-208.
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.
[[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.]]
Submitted (in 2nd revision) to the American Journal of Sociology. Douglas R. White, Michael Schnegg, Lilyan A. Brudner, and Hugo G. Nutini. "Multiple Connectivity, its Boundaries and Limits of Integration: Social Cohesion and Social Class in Tlaxcala"
2002 "Conectividad Múltiple, Fronteras e Integración: Compadrazgo y Parentesco en Tlaxcala Rural" (drw, Michael Schnegg, Lilyan Brudner & Hugo G. Nutini), pp. 41-94, Análisis de Redes: Aplicaciones en Ciencias Sociales, Eds. Jorge Gil-Mendieta y Samuel Schmidt. Mexico, D.F.: IIMAS- UNAM. (Instituto de Investigaciones en Mathemáticas Aplicadas y en Systemas- Universidad Nacional Autónoma de México)
Abstract. 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.
1998 Michael Houseman and Douglas R. White, "Taking Sides: Marriage Networks and Dravidian Kinship in Lowland South America," Transformations of Kinship, pp. 214-243 in eds. Maurice Godelier, Thomas Trautmann and F.Tjon Sie Fat, Smithsonian Institution Press.
Editors' Summary: "Michael Houseman and Douglas R. White develop a new method of representing Dravidian-like kinship systems that visually renders both empirical cases and ideal-type models -- the "statistical" and "mechanical" models of Lévi-Strauss's well-known discussion (1969:xxvii ff.) -- in the same register, so that they can be directly compared. They introduce into the discussion of Dravidianate systems a rigorous graphic modeling of actual marriage networks that is based on their conception of "sidedness," which occupies a middle ground between the egocentric structures of the kinship terminology and sociocentric structures of social groups, such as moieties and section systems. Their elegant new instrument has a number of promising applications in kinship studies." (Editors, p. 14)
1999. Douglas R. White, Vladimir Batagelj and Andrej Mrvar, "Analyzing Large Kinship and Marriage Networks with Pgraph and Pajek," Social Science Computer Review 17(3):245-274.
The p-graph approach that has proven an invaluable aid to the study of kinship, marriage and genealogical network analysis here is explicated – 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.
1998 Thomas Schweizer and Douglas R. White, "Revitalizing the Study of Kinship and Exchange with Network Approaches," pp. 1-9. in Kinship, Networks, and Exchange, eds. Thomas Schweizer and Douglas R. White. Cambridge University Press.
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.
1999 Douglas R. White, "The Invisible State: Low Density Multiconnected Cohesion in Large-Scale Social Networks in Tlaxcala, Mexico ," Irvine Conference on Decentralized Systems organized by Art De Vany and William Batchelder
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:
Keywords: Graph theory, social networks, algorithmic detection, cohesive groups, social boundaries
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.
1998 Michael Houseman and Douglas R. White, " Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya," pp. 59-89. in Kinship, Networks, and Exchange, eds. Thomas Schweizer and Douglas R. White. Cambridge University Press.
Using Galois Lattices to Represent Network Data Freeman L C, White D R Sociological Methodology 1993, Vol 23 Sociological Methodology 23: 127-146 1993
Betweeness Centrality Measures for Directed-Graphs White D R, Borgatti S P Social Networks 16 (4): 335-346 Oct 1994
Structure and Dynamics of the Global Economy - Network Analysis of International-Trade 1965-1980 Smith D A, White D R Social Forces 70 (4): 857-893 Jun 1992
Statistical Entailments and the Galois Lattice White D R Social Networks 18 (3): 201-215 Aug 1996
Network structures of marriage practice Houseman M, White D R L'Homme 36 (139): 59-85 Jul-Sep 1996
Kinship networks and discrete structure theory: Applications and implications White D R, Jorion P Social Networks 18 (3): 267-314 Aug 1996
Anthropology - Analyzing large kinship and marriage networks with Pgraph and Pajek White D R, Batagelj V, Mrvar A Social Science Computer Review 17 (3): 245-274 Fall 1999
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