In their previous book, , Hage and Haray used graph theory, a branch of pure mathematics, to develop a family of models for the study of social, symbolic, and cognitive relations. With the authors extend these models using ethnographic data from Melanesia, Micronesia, and Polynesia to demonstrate that the language, techniques, and theorems 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.