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This is a peer-reviewed journal with articles in French and English.
Mathematical Anthropology and Culture Theory. This is an online, peer-reviewed journal devoted to the scientific study of culture, with a focus on mathematical anthropology and culture theory.
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Journals There is a single journal, Mathematical Anthropology and Culture Theory , devoted to mathematical anthropology. How to Subscribe Oxford Bibliographies Online is available by subscription and perpetual access to institutions. In Handbook of social and cultural anthropology. Edited by J. Honigmann, — Chicago: Rand McNally. An extensive review article that considers four ways mathematical concepts may be applied to anthropology: processual analysis, optimization analysis, structural analysis, and ethnographic decomposition.
Graph Theory and Structural Models Graph theory is another branch of mathematics that has been used to represent the structural properties of human societies. The mathematical properties of graphs—where a graph is a structure consisting of a set of nodes and connections between nodes, referred to as edges —was developed extensively by the mathematician Harary and then introduced into anthropology through his long collaboration with the anthropologist Per Hage.
Together, they wrote three books relating graph theory to the structures of interest to cultural anthropologists. This book also shows how graph theory representations make it possible to work out the implications of ideas and analytical arguments developed by cultural anthropologists regarding cultural systems. Graph theory, for Hage, enables rigorous engagement in cross-cultural comparison and theorizing. Their second book focuses on exchange systems found in the Oceanic societies and shows that dual forms of social organization can be more precisely represented through a bipartite graph.
A bipartite graph is a graph G, in which there are two sets of nodes, G1 and G2, with every node in G1 connected by an edge to a node in G2 and vice-versa. A significant part of this book is their study of the kula ring discussed by Bronislaw Malinowski and represented by them through graphs.
Their book also includes a discussion of pollution beliefs in Mount Hagen in Highland New Guinea as a transformation group, thus identifying another area, in addition to the marriage rules of Australia, where the mathematical concept of permutation groups is relevant to representing a structure that is part of a cultural domain. Their third book uses the graph concept of a tree to represent the Yapese prestige-good systems that connected twenty islands scattered over kilometers of ocean. They also show how to formally characterize what has been referred to as a conical clan.
Exchange in Oceania: A graph theoretic analysis. Oxford: Clarendon Press. Second of three books written in collaboration with Harary, a mathematician. This book focuses on Oceanic trading systems, especially the kula ring discussed by Malinowski. Island networks: Communication, kinship, and classification structures in Oceania. New York: Cambridge Univ.
Third of three books written in collaboration with Harary, a mathematician. Uses tree graphs to represent the Yapese system of exchange of prestige goods and shows the commonality among what has been characterized as different forms of social organization among Oceanic peoples. Social Network Analysis and Graph Theory The use of social networks in research is widespread in the behavioral sciences. Social networks connect analytically the phenomenal level of behavior to the ideational and formal level of representation of cultural idea systems.
According to Borgatti, et al.
As discussed in Hanneman and Riddle , the data for social network analysis consists of networks with nodes made up of individuals, or groups of individuals, with connections, or edges, between nodes formed through behavior. A social network is not inherently mathematical in the sense, as discussed in Leaf and Read cited under Formalization Based on Primary Cultural Concepts , that the structure and organization of cultural idea systems can be expressed mathematically.
Consequently, though the structure of social networks, as discussed in Wasserman and Faust , is describable using mathematical concepts and mathematical notation, social networks do not arise through the instantiation of cultural processes as is the case with cultural idea systems. Instead, the analysis presented by Wasserman and Faust focuses on discerning patterning in the social ties connecting one individual to another. Formal mathematical concepts used in graph theory and matrix algebra operations are used to express concepts relating to the structure and organization of a social network.
Social network analysis, then, involves working out the implications arising from both the structure of a network formed from social ties among actors and the position of nodes, representing actors, within the social network. Social networks may be represented visually through a graph in which the nodes are the actors and the edges of the graph represent the social ties among the actors, or alternatively through an adjacency matrix.
Ways in which the formalisms of graph theory and of matrix algebra are relevant to the representation of networks and to the discernment and interpretation of patterning in social networks are discussed in Wasserman and Faust Since analysis aimed at discerning pattern in social networks is computationally intensive, a variety of computer software packages have been developed to aid in both the display of networks and the analysis of network data. The computer program Pajek, discussed in De Nooy, et al.
Borgatti, Stephen P. Everett, and Lynn C. Harvard, MA: Analytic Technologies. Everett, and Jeffrey C. Analyzing social networks. A good text for introducing researchers without a background in network analysis to the core methods for collecting, visualizing, analyzing, and interpreting social network data. The text covers the theory and analytical procedures used in doing social network analysis. Written with simple language, the text discusses each of steps and basic mathematical principles involved in social network analysis.
Exploratory social network analysis with Pajek. The software program Pajek makes possible the exploratory analysis of large-scale social networks. The book is clearly written with numerous examples. The authors present ways to explore social networks visually using Pajek in order to identify meaningful patterns in the social network of concern. Pajek may be downloaded from the website located online. Hanneman, Robert A.
Though no base is used in this system, it is adequate when trading goods using a one-to-one correspondence. Lawvere, F. Development in Brown , by Wassily Kandinsky. Meet the Staff Partners. Patterns of Thought. View on ScienceDirect. Growth Patterns of Fields of Mathematics
Introduction to social network methods. Riverside, CA: Univ. An online textbook that introduces some of the formal methods used in the analysis of social networks. The text may be downloaded online. Wasserman, Stanley, and Katherine Faust. Social network analysis: Methods and applications. A basic and widely referenced text for the methods and ideas used in the analysis, representation, and interpretation of social networks.
Social Network Analysis: Connecting Practice with Theory Social network analysis connects behaviorally based networks with structures determined through formal properties. This connection is described and implemented in Lorrain and White for detailed social networks. The authors determine global patterning from classes of individuals positioned equivalently in the network. A key aspect of their approach is the distinction between relations connecting the individuals upon which a social network is based and the social positions occupied by these individuals.
The global pattern is determined from a social network through structural simplification based on algebraic properties of structures developed in category theory, a branch of mathematics concerned with formal properties common to all algebraic structures. While Lorrain and White make no a priori assumptions about a social network, the kinship domain genealogies, viewed as social networks, are based on the presumption that marriage and reproduction are central properties. Genealogical diagrams, as pointed out in White and Jorion , impose a western notion of individualism on kinship relations.
Examples showing how P-graphs make structure evident in networks of actual marriage relations are provided in Housemann and White Thus, sidedness may be emergent and not just rule driven. Housemann, Michael, and Douglas White. Taking sides: Marriage networks and Dravidian kinship in lowland South America. In Transformations of Kinship. The authors examine the structural pattern of actual marriage networks as a way to consider the relationship between the structural pattern of social networks and aspects of social organization.
They derive new results regarding kinship systems based on dual organization. Structural equivalence of individuals in social networks. Journal of Mathematical Sociology 1. Rather than starting with ideal types of structures and mapping these onto data, the authors begin with empirical social networks and work out global structure from the network by identifying classes of individuals determined to be in structurally equivalent positions in the network.
Their algebraic analysis of social networks determines a global network of relations from an empirically determined social network. Tjon Sie Fat considers the logic of parallel same sex and cross opposite sex sibling connections in genealogical pathways.