A graph theoretic approach to the analysis of alliance structure and local grouping in highland New Guinea 1

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Abstract
This paper focuses on a set of structural properties which characterize the Gahuku‐Gama, a social and cultural unit in the Eastern Central Highlands of New Guinea. Gahuku‐Gama “society” has been described as a finite network, the members of which are social groups connected by bonds of traditional warfare and alliance. The aims of the paper are (1) to formalize some ordinary English terms which have been applied to this system; (2) to elucidate these properties through the application of graph theoretic concepts and theorems; (3) to use certain of these theorems in the prediction of empirical facts of local grouping; and (4) to suggest that this approach could usefully be adopted in relation to similar sociocultural systems in Highland New Guinea and elsewhere.