The cover time of a sparse random intersection graph

TL;DR

This paper analyzes the cover time of simple random walks on sparse random intersection graphs, a model for affiliation networks, especially at and above the connectivity threshold.

Contribution

It establishes the cover time behavior of random walks on the binomial random intersection graph at critical connectivity thresholds.

Findings

Cover time is characterized at the connectivity threshold.

Results apply to networks where attributes are shared by a bounded number of actors.

Provides insights into random walk dynamics on sparse affiliation networks.

Abstract

Many known networks have structure of affiliation networks, where each of $n$ network's nodes (actors) selects an attribute set from a given collection of $m$ attributes and two nodes (actors) establish adjacency relation whenever they share a common attribute. We study behaviour of the random walk on such networks. For that purpose we use commonly used model of such networks -- random intersection graph. We establish the cover time of the simple random walk on the binomial random intersection graph ${\cal G}(n,m,p)$ at the connectivity threshold and above it. We consider the range of $n,m,p$ where the typical attribute is shared by (stochastically) bounded number of actors.