Exchange in Oceania: A Graph Theoretic Analysis / Edition 1

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Exchange in Oceania contains a rich and varied repertory of structural models applied to a fascinating array of exchange systems. The book will provide a sound general foundation for future research on exchange relations.
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Product Details

Meet the Author

University of Utah

New Mexico State University

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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
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