Hidden Variables in Bipartite Networks

TL;DR

This paper introduces a hidden variable framework for bipartite networks, deriving analytical expressions for key topological properties and validating them through simulations.

Contribution

It presents a novel analytical approach to characterize bipartite networks with hidden variables, linking degree distributions and correlations to underlying node attributes.

Findings

Derived formulas for degree distribution and correlations

Established relationships between bipartite and projected networks

Validated analytical results with numerical simulations

Abstract

We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables which control the appearance of links between node pairs. We derive analytic expressions for the degree distribution, degree correlations, the distribution of the number of common neighbors, and the bipartite clustering coefficient in these networks. We also establish the relationship between degrees of nodes in original bipartite networks and in their unipartite projections. We further demonstrate how hidden variable formalism can be applied to analyze topological properties of networks in certain bipartite network models, and verify our analytical results in numerical simulations.