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Preface Acknowledgements 1. Island networks and graphs - graph theoretical models - geographical, linguistic and anthropological terms 2. Trees: Basic definitions - a Micronesian prestige good system - 'Recursive dualism' in Austronesian classification systems - cognatic kinship networks - cycle rank and network connectedness 3. The minimum spanning tree problem - dialect groups and marriage isolates in the Tuamotus - the evolution of the Lakemban Matanitu - the Renfrew-Sterud method of close proximity analysis - on deconstructing a network 4. Search trees I: Independent discoveries of the conical clan - social stratification in Polynesia - a structural model of the conical clan - Prestige good systems: 5. Search trees II: the Marshallese conical clan - the devolution of social organisation in nuclear Micronesia;6. Centrality: Southern Lau, Fiji: a natural trade area - power centers in the greater Lauan trade network - political and mythological centers in Ralik and Ratak - expeditions in Torres Strait - on the position of Delos in the archaic Aegean network 7. Dominating sets: local domination in the Caroline Islands - alliance structures in the Western Tuamotus - pottery monopolies in Melanesian trade networks 8. Digraphs: Murdock's maze: the bilateral hypothesis of Austronesian origins - sibling classification and culture history in Island Oceania 9. Conclusion.