In a previous work, anthropologist Per Hage and mathematician Frank Harary used graph theory, a branch of pure mathematics, to develop a family of models for the study of social, symbolic and cognitive relations. In this new book they extend these models and apply them to the analysis of exchange structures in Oceania, presenting graph theory in a form accessible to the non-mathematical reader. Using ethnographic data from Melanesia, Micronesia and Polynesia, they attempt to demonstrate that the language, techniques and theorums 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. The work is aimed at teachers and postgraduate students of anthropology - in particular social network analysts and Oceanists, sociologists, economists, mathematicians, geographers, philosophers, linguists, historians who focus on this area, and computer scientists.

In their previous book, Exchange in Oceania, anthropologist Per Hage and mathematician Frank Harary demonstrated that models from graph theory, a branch of pure mathematics, provide the essential basis for analyzing the great variety of exchange systems in Micronesian, Melanesian, and Polynesian societies. In this new book the authors extend these models and apply them to the analysis of communication, kinship, and classification structures in the island societies of Oceania, presenting the relevant topics from graph theory in a form accessible to the nonmathematical reader. The research problems include the formation of island empires, the social basis of dialect groups, the emergence of trade and political centers, the evolution and devolution of social stratification, the transformations of marriage and descent systems, the historical development of kinship terminologies, and the reconstruction of protosocieties.

Contrary to common perception and belief, most island societies of the Pacific were not isolated, but were connected to other island societies by relations of kinship and marriage, trade and tribute, language and history. Using network models from graph theory the authors analyze the formation of island empires, dialect groups, economic and political centers; the evolution and devolution of social stratification; and the development of kinship terminologies, marriage systems and descent groups.

Hage and Harary present a comprehensive introduction to the use of graph theory in social and cultural anthropology. Using a wide range of empirical examples, the authors illustrate how graph theory can provide a language for expressing in a more exact fashion concepts and notions that can only be imperfectly rendered verbally. They show how graphs, digraphs and networks, together with their associated matrices and duality laws, facilitate the study of such diverse topics as mediation and power in exchange systems, reachability in social networks, efficiency in cognitive schemata, logic in kinship relations, and productivity in subsistence modes. The interaction between graphs and groups provides further means for the analysis of transformations in myths and permutations in symbolic systems. The totality of these structural models aids in the collection as well as the interpretation of field data. The presentation is clear, precise and readily accessible to the nonmathematical reader. It emphasizes the implicit presence of graph theory in much of anthropological thinking.