Degree distributions of bipartite networks and their projections

TL;DR

This paper analyzes how the degree distributions of bipartite networks influence their one-mode projections, revealing that the projection's degree distribution depends on both node types' distributions and challenging previous assumptions.

Contribution

It provides a broader theoretical framework using generating functions to understand the impact of both node types' degree distributions on projected network topology.

Findings

Degree distribution of projected network follows the distribution of projected nodes if the opposite set has a lighter tail.

Heavy-tailed degree distributions in the opposite set alter the projected network's degree distribution.

Bipartite degree distributions are not the sole factors influencing the topology of projected networks.

Abstract

Bipartite (two-mode) networks are important in the analysis of social and economic systems as they explicitly show conceptual links between different types of entities. However, applications of such networks often work with a projected (one-mode) version of the original bipartite network. The topology of the projected network, and the dynamics that take place on it, are highly dependent on the degree distributions of the two different node types from the original bipartite structure. To date, the interaction between the degree distributions of bipartite networks and their one-mode projections is well understood for only a few cases, or for networks that satisfy a restrictive set of assumptions. Here we show a broader analysis in order to fill the gap left by previous studies. We use the formalism of generating functions to prove that the degree distributions of both node types in the original bipartite network affect the degree distribution in the projected version. To support our analysis, we simulate several types of synthetic bipartite networks using a configuration model where node degrees are assigned from specific probability distributions, ranging from peaked to heavy-tailed distributions. Our findings show that when projecting a bipartite network onto a particular set of nodes, the degree distribution for the resulting one-mode network follows the distribution of the nodes being projected on to, but only so long as the degree distribution for the opposite set of nodes does not have a heavier tail. Furthermore, we show that bipartite degree distributions are not the only feature driving topology formation of projected networks, in contrast to what is commonly described in the literature.