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 |