Cycles and clustering in bipartite networks

TL;DR

This paper introduces a new clustering coefficient for bipartite networks based on four-cycles, compares it with the standard coefficient, and provides an improved method for estimating larger cycles, applicable to various network types.

Contribution

It proposes a novel clustering coefficient for bipartite networks, demonstrating its equivalence to the standard measure and developing an improved cycle estimation method.

Findings

The new coefficient aligns with the standard clustering measure in bipartite networks.

Clustering abilities are similar in monopartite and bipartite sexual contact networks.

The combined coefficients enable better estimation of larger cycles in different network types.

Abstract

We investigate the clustering ability 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 monopartite and another bipartite. In both cases the clustering ability 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.