Joint Probability Generating Function for Degrees of Active/Passive Random Intersection Graphs

TL;DR

This paper derives the joint probability generating function for degrees in active and passive random intersection graphs, revealing their correlation structure based on a bipartite graph model.

Contribution

It introduces a joint probability generating function for degrees in active/passive intersection graphs, advancing understanding of their correlation properties.

Findings

Provides the explicit joint probability generating function

Analyzes degree correlations in intersection graphs

Enhances modeling of bipartite graph-based networks

Abstract

Correlations of active and passive random intersection graphs are studied in this letter. We present the joint probability generating function for degrees of $G^{active}(n,m,p)$ and $G^{passive}(n,m,p)$, which are generated by a random bipartite graph $G^*(n,m,p)$ on $n+m$ vertices.