The structure of animal societies impacts components of fitness, including survival, sexual selection, and reproductive success. Social structure is also instrumental to understanding of disease and cultural transmission, and the evolution of cooperation. Recent studies of animal sociality found multiple factors affecting social structure, but most of them used static social networks, ignoring temporal dynamics. I will describe a study of the environmental, individual, genetic, and structural factors that influence social network dynamics in spotted hyenas over 20 years, the largest such analysis to date. This study demonstrates that topological factors constrain the network dynamics, suggesting that some network structures are more stable than others. Next, I will present a general model of the dynamics of animal social networks, based on demographic stochasticity and social inheritance. This model can reconstruct the observed networks of multiple species. The model also suggests that heritability of social traits, and assortativity, the tendency to connect to similar individuals, can be explained as byproducts of social inheritance. Taken together, my results demonstrate the importance of clustering to the stability of social structure, and promote the move from observing patterns to understanding processes of animal sociality.