Exchange in Oceania: A Graph Theoretic Analysis(Oxford Studies in Social and Cultural Anthropology)

In their previous book, Structural Models in Anthropology, anthropologist Per Hage and mathematician Frank Harary used graph theory, a branch of pure mathematics, to develop a family of models for the study of social, symbolic, and cognitive relations. In this book the authors extend these models and apply them to the analysis of exchange structures in Oceania, presenting graph theory in a form accessible to the non-mathematical reader. Using ethnographic data from Melanesia, Micronesia, and Polynesia, they demonstrate that the language, techniques, and theorems of graph theory provide the essential basis for the description, quantification, simulation, enumeration, and notation of the great variety of exchange forms actually found in Oceanic societies.

Table of Contents:
Graph theory and exchange structures: primordial structures; necessary relations; graphs and their uses; set theoretic concepts; Paths, cycles, and partitions: basic definitions; bipartite graphs and dual organization; colourable signed graphs and competitive exchange; ceremonial analogues of marriage exchange; exchange quartets; Centres, neighbourhoods, and roots: voyaging, exchange, and stratification in the Caroline Islands; rooted graphs and island settlement patterns in Micronesia; Matrix analysis: matrix representation; matrix operations; 'connectivity analysis' in Melanesian archaeology; geodetic structure; Melanesian exchange networks; evolution of trade networks; Markov chains: wealth and hierarchy in the Kula ring; alternative Kula rings; the UrKula ring; models of social, trade, and transport networks; Combination and enumeration: exchange dualities; an atom of kinship: Arapesh; Tonga; structuralistes avant la lettre; structures en creux; on a 'calculus' of Melanesian exchange structures; Binary operations and groups: a Micronesian anatomy graph; notation of exchange structures; pollution beliefs in highland New Guinea; Logic of relations: relations and graphs; network vs. relations; relation: Siassi marriage exchange; digraph: Rossel Island marriage exchange; graph: Lesu marriage exchange; oriented graph: Carolinian tribute relations; Similarity relation: Trukic dialect chain; equivalence relation: neighbourhood of a dialect; orders: big man, chief; tournament: the Tongan solution; parity relation: inner structure; antiequivalence relation: ritual exchange; antiparity relation: whales' teeth, turtles, pigs, and men

Review :
`Most illuminating ... [presents] a formalism easy to grasp, which enables one to reduce to common terms several approaches apparently different from each other. This represents a major breakthrough: it clears the ground for a generalized theory of exchange relationships ... a great achievement.' Claude Lévi-Strauss, Honorary Professor, Collège de France 'Hage and Harary find in graph theory a way of uncovering underlying similarities of structure between kinship structures and other structures of exchange as diverse as the kula ring and the atom of kinship ... they take the greatest step forward since Lévi-Strauss published Les Structures Élémentaires in 1949 ... This book is more than simply a contribution to "mathematical anthropology" but a mainstream contribution in the noblest traditions of the subject.' Robin Fox, University Professor of Social Theory, Rutgers University 'This is a remarkable book which presents a fascinating mixture of anthropology and graph theory. The whole volume is full of innovative ideas and thought-provoking examples. The book is so carefully prepared and so lucidly presented that a reviewer really only needs to make a careful selection of excerpts in order to give the flavour of the work. It is a truly masterful opus that combines interest and utility.' `This is a remarkable book which presents a fascinating mixture of anthropology and graph theory ... The whole volume is full of innovative ideas and thought-provoking examples. The work is a worthy successor to the earlier Hage-Harary volume on Structural Models in Anthropology (1983). The authors summarize their own work admirably ... The book is so carefully prepared and so lucidly presented that a reviewer really only needs to make a careful selection of excerpts in order to give the flavour of the work. It is a truly masterful opus that combines interest and utility.' Bulletin of the Institute of Cominatorics and its Applications `Hage and graph-theorist Harary provide foundations for the comprehensive study of structure and dispel some conceptual confusions haunting ethnographic literature ... they demonstrate what we can learn by an explicit formulation of concepts, directed toward robust substantive application.' American Anthropologist