Random intersection graphs with tunable degree distribution and clustering

Authors:
Maria Deijfen;Willemien Kets
Affiliations:
Department of mathematics, stockholm university, 106 91 stockholm, sweden e-mail: mia@math.su.se;Santa fe institute, 1399 hyde park road, santa fe, nm 87501 andcenter, tilburg university, p.o. box 90153, 5000 le tilburg, netherlands e-mail: willemien.kets@santafe.edu
Venue:
Probability in the Engineering and Informational Sciences
Year:
2009

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Abstract

A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this article a model is developed in which each vertex is given a random weight and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a given vertex is characterized and is shown to depend on the weight of the vertex. In particular, if the weight distribution is a power law, the degree distribution will be as well. Furthermore, an asymptotic expression for the clustering in the graph is derived. By tuning the parameters of the model, it is possible to generate a graph with arbitrary clustering, expected degree, and—in the power-law case—tail exponent.