Exchange in Oceania: A Graph Theoretic Analysis / Edition 1

Exchange in Oceania: A Graph Theoretic Analysis / Edition 1

by Per Hage, Frank Harary
     
 

ISBN-10: 0198277601

ISBN-13: 9780198277606

Pub. Date: 07/28/1991

Publisher: Oxford University Press, USA

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

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, USA
Publication date:
07/28/1991
Series:
Oxford Studies in Social and Cultural Anthropology Series
Pages:
336
Product dimensions:
5.69(w) x 8.81(h) x 1.01(d)

Table of Contents

1Graph Theory And Exchange Structures1
Prologue2
Primordial structures6
Necessary relations9
Graphs and their uses12
Set theoretic concepts27
2Paths, Cycles, And Partitions30
Basic definitions30
Bipartite graphs and dual organization36
Colourable signed graphs and competitive exchange49
Ceremonial analogues of marriage exchange54
Exchange quartets70
3Centres, Neighbourhoods, and Roots72
Voyaging, exchange, and stratification in the Caroline Islands74
Rooted graphs and island settlement patterns in Micronesia103
4Matrix Analysis115
Matrix representation116
Matrix operations120
'Connectivity analysis' in Melanesian archaeology123
Geodetic structure134
The raw and the cooked: Hierarchy and intimacy in Melanesian exchange networks136
Nearest neighbours and the evolution of trade networks146
Evolutionary trees in exchange networks153
5Markov Chains156
Wealth and hierarchy in the kula ring156
Alternative kula rings170
A speculation on the Ur-kula ring171
On models of social, trade, and transport networks173
6Combination And Enumeration177
Exchange dualities179
An atom of kinship: Arapesh182
A generalized atom of kinship: Tonga191
Structuralistes avant la lettre198
Structures en creux204
On a 'calculus' of Melanesian exchange structures209
7Binary Operations And Groups215
A Micronesian anatomy graph216
On the notation of exchange structures224
Pollution beliefs in Highland New Guinea227
8Logic Of Relations240
Relations and graphs241
Networks vs. relations247
Relation: Siassi marriage exchange249
Digraph: Rossel Island marriage exchange250
Graph: Lesu marriage exchange252
Oriented graph: Carolinian tribute relations252
Similarity relation: The Trukic dialect chain254
Equivalence relation: The neighbourhood of a dialect258
Orders: Big man, chief260
Tournament: The Tongan solution263
Parity relation: Inner structure268
Antiequivalence relation: Ritual exchange269
Antiparity relation: Whales' teeth, turtles, pigs, and men271
Conclusion272
Appendix 1Table of named sea-lanes in the Carolines and Marianas276
Appendix 2Simulations of alternative kula rings282
Appendix 3The geodesic counting matrix of a graph285
Appendix 4Reference list of theorems and proofs287
Bibliography293
Index313

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