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

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.