Representing Small Group Evolution

Understanding the dynamics of network evolution rests in part on the representation chosen to characterize the evolutionary process. We offer a simple, three-parameter representation based on subgraphs that capture three important properties of social networks: leadership, team alignment or bonding among members, and diversity of expertise. When plotted on this representation, the evolution of a typical small group such as start-ups or street gangs has a spiral trajectory, moving toward a tentative fixed point as membership increases to two dozen or so. We show that a simple probabilistic model for recruitment and bonding can not explain these observations, and suggest that strategic moves among group members may come into play.