Scale free projections arise from bipartite random networks

Abstract The degree distribution of a real world network—the number of links per node—often follows a power law, so some hubs have many more links than traditional graph generation methods predict. For years, preferential attachment and growth have been the proposed mechanisms that lead to these scale free networks. However, when two sides of bipartite graphs like collaboration networks are not scale free, they are not well-explained by these processes. Here we develop a bipartite extension to the Randomly Stopped Linking Model for generating networks and show that mixtures of geometric distributions can lead to power laws, an intuition suggested by the Central Limit Theorem for distributions with infinite variance. We show that the two halves of the actor–movie network are not scale free and can be represented by just 6 geometric distributions, but they combine to form a scale free actor–actor unipartite projection without preferential attachment or growth. This result supports our claim that scale free networks are the natural result of many Bernoulli trials with high variance of which preferential attachment and growth are only one example.