Cycles and clustering in bipartite networks

Abstract

We investigate the clustering coefficient in bipartite networks where cycles of size three are absent and therefore the standard definition of clustering coefficient cannot be used. Instead, we use another coefficient given by the fraction of cycles with size four, showing that both coefficients yield the same clustering properties. The new coefficient is computed for two networks of sexual contacts, one bipartite and another where no distinction between the nodes is made (monopartite). In both cases the clustering coefficient is similar. Furthermore, combining both clustering coefficients we deduce an expression for estimating cycles of larger size, which improves previous estimations and is suitable for either monopartite and multipartite networks, and discuss the applicability of such analytical estimations.