The complexity of social networks: theoretical and empirical findings

A great deal of work in recent years has been devoted to the topic of \complexity,' its measurement, and its implications. Here, the notion of algorithmic complexity is applied to the analysis of social networks. Structural features of theoretical importance such as structural equivalence classes are shown to be strongly related to the algorithmic complexity of graphs, and these results are explored using analytical and simulation methods. Analysis of the complexity of a variety of empirically derived networks suggests that many social networks are nearly as complex as their source entropy, and thus that their structure is roughly in line with the conditional uniform graph distribution hypothesis. Implications of these ndings for network theory and methodology are also discussed.