Abstract
Many known networks have structure of affiliation networks, where each of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> network nodes (actors) selects an attribute set from a given collection of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> attributes, and two nodes (actors) establish adjacency relation whenever they share a common attribute. We study the behavior of a random walk on such networks. For this purpose, we use a common model of such networks, a random intersection graph. We establish the cover time of the simple random walk on the binomial random intersection graph <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ G}}(n,m,p)$ </tex-math></inline-formula> at the connectivity threshold and above it. We consider the range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(n,m,p)$ </tex-math></inline-formula> , where the typical attribute is shared by a (stochastically) bounded number of actors.
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