Over a long and productive career, Per Hage produced a diverse and influential body of work. He conceptualized and solved a range of anthropological problems, often with the aid of mathematical models from graph theory. In three books and many research articles, Hage, and his mathematician collaborator Frank Harary, developed innovative analyses of exchange relations, including marriage, ceremonial, and resource exchange. They advanced network models for the study of communication, language evolution, kinship and classification. And they demonstrated that graph theory provides an analytical framework that is both subtle enough to preserve culturally specific relations and abstract enough to allow for genuine cross-cultural comparison. With graph theory, two common analytical problems in anthropology can be avoided: the problem of hiding cultural phenomena with weak cross-cultural generalizations, and the problem of making misleading comparisons based on incomparable levels of abstraction. This paper provides an overview of Hage’s work in an attempt to place it in the broader context of anthropology in the latetwentieth and early-twenty first centuries.