The human ability to form large, coordinated groups is among our most impressive social adaptations. Larger groups facilitate synergistic economies of scale for cooperative breeding, such economic tasks as group hunting, and success in conflict with other groups. In many organisms, genetic relationships provide the structure for sociality to evolve via the process of kin selection, and this is the case, to a certain extent, for humans. But assortment by genetic affiliation is not the only mechanism that can bring people (...) together. Affinity based on symbolically mediated and socially constructed identity, or cultural kinship, structures much of human ultrasociality. This paper examines how genetic kinship and two kinds of cultural kinship—affinal kinship and descent—structure the network of cooperating whale hunters in the village of Lamalera, Indonesia. Social network analyses show that each mechanism of assortment produces characteristic networks of different sizes, each more or less conducive to the task of hunting whales. Assortment via close genetic kin relationships (r = 0.5) produces a smaller, denser network. Assortment via less-close kin relations (r = 0.125) produces a larger but less dense network. Affinal networks are small and diffuse; lineage networks are larger, discrete, and very dense. The roles that genetic and cultural kinship play for structuring human sociality is discussed in the context of these results. (shrink)