P-Systems: A Structural Model for Kinship Studies

CONNECTIONS 24(2): 35-46 © 2001 INSNA P-Systems: A Structural Model for Kinship Studies Frank Harary Department of Computer Science, New Mexico State University Douglas R. White 1 Department of Anthropology, University of California, Irvine November 15, 2000 We dedicate this paper to the memory of Oystein Ore 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 Levi-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. Introduction Several mathematical models have been proposed for kinship studies. Those that are sufficiently general to allow a network analysis of kinship and marriage or the recording of genealogical data include the genetic graph proposed by the great Norwegian mathematician Oystein Ore (1960), the FH Fax 505 646 6218; DW Fax 949 824 4717. This research was supported by NSF Award BCS-9978282 (1999-2001) to Douglas White, Longitudinal Network Studies and Predictive Social Cohesion Theory, with Frank Harary as consultant.

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