Exchange in Oceania: A Graph Theoretic Analysis / Edition 1

by Per Hage, Frank Harary

Overview

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.

Product Details

ISBN-13:	9780198277606
Publisher:	Oxford University Press
Publication date:	10/10/1991
Series:	Oxford Studies in Social and Cultural Anthropology
Pages:	336
Product dimensions:	5.69(w) x 8.81(h) x 1.02(d)

About the Author

University of Utah

New Mexico State University

Table of Contents

1	Graph Theory And Exchange Structures	1
	Prologue	2
	Primordial structures	6
	Necessary relations	9
	Graphs and their uses	12
	Set theoretic concepts	27
2	Paths, Cycles, And Partitions	30
	Basic definitions	30
	Bipartite graphs and dual organization	36
	Colourable signed graphs and competitive exchange	49
	Ceremonial analogues of marriage exchange	54
	Exchange quartets	70
3	Centres, Neighbourhoods, and Roots	72
	Voyaging, exchange, and stratification in the Caroline Islands	74
	Rooted graphs and island settlement patterns in Micronesia	103
4	Matrix Analysis	115
	Matrix representation	116
	Matrix operations	120
	'Connectivity analysis' in Melanesian archaeology	123
	Geodetic structure	134
	The raw and the cooked: Hierarchy and intimacy in Melanesian exchange networks	136
	Nearest neighbours and the evolution of trade networks	146
	Evolutionary trees in exchange networks	153
5	Markov Chains	156
	Wealth and hierarchy in the kula ring	156
	Alternative kula rings	170
	A speculation on the Ur-kula ring	171
	On models of social, trade, and transport networks	173
6	Combination And Enumeration	177
	Exchange dualities	179
	An atom of kinship: Arapesh	182
	A generalized atom of kinship: Tonga	191
	Structuralistes avant la lettre	198
	Structures en creux	204
	On a 'calculus' of Melanesian exchange structures	209
7	Binary Operations And Groups	215
	A Micronesian anatomy graph	216
	On the notation of exchange structures	224
	Pollution beliefs in Highland New Guinea	227
8	Logic Of Relations	240
	Relations and graphs	241
	Networks vs. relations	247
	Relation: Siassi marriage exchange	249
	Digraph: Rossel Island marriage exchange	250
	Graph: Lesu marriage exchange	252
	Oriented graph: Carolinian tribute relations	252
	Similarity relation: The Trukic dialect chain	254
	Equivalence relation: The neighbourhood of a dialect	258
	Orders: Big man, chief	260
	Tournament: The Tongan solution	263
	Parity relation: Inner structure	268
	Antiequivalence relation: Ritual exchange	269
	Antiparity relation: Whales' teeth, turtles, pigs, and men	271
	Conclusion	272
Appendix 1	Table of named sea-lanes in the Carolines and Marianas	276
Appendix 2	Simulations of alternative kula rings	282
Appendix 3	The geodesic counting matrix of a graph	285
Appendix 4	Reference list of theorems and proofs	287
	Bibliography	293
	Index	313

Editorial Reviews

"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

From the Publisher