Exchange in Oceania
A Graph Theoretic Analysis
Series: Oxford Studies in Social and Cultural Anthropology;
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Product details:
- Publisher Clarendon Press
- Date of Publication 29 August 1991
- ISBN 9780198277606
- Binding Hardback
- No. of pages334 pages
- Size 223x143x25 mm
- Weight 564 g
- Language English
- Illustrations numerous line figures and tables 0
Categories
Short description:
The authors 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.
MoreLong description:
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.
`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, Coll?ge de France
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
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