Exchange in Oceania: A Graph Theoretic Analysis

ISBN-13: 9780198277606 / Angielski / Twarda / 1991 / 336 str.

Per Hage; Frank Harary

Opis

In their previous book, Structural Models in Anthropology, Hage and Haray used graph theory, a branch of pure mathematics, to develop a family of models for the study of social, symbolic, and cognitive relations. With Exchange in Oceania the authors extend these models using ethnographic data from Melanesia, Micronesia, and Polynesia to 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.

Recenzje

`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

Spis treści

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