Random intersection graphs with tunable degree distribution and clustering

Journal article

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, andin the power-law casetail exponent. © 2009 Cambridge University Press.

Authors: Deijfen, M; Kets, W

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Probability in the Engineering and Informational Sciences
• Volume: 23
• Issue: 4
• Pages: 661-674
• Article number: 2007-008
• Series: CentER Discussion Paper
• Publication date: 2009-07-14
• Event start date: 2007
• DOI: 10.1017/S0269964809990064
• EISSN: 1469-8951
• ISSN: 0269-9648
• Language: English
• Keywords: SBTMR; Z13; Random intersection graphs; degree distribution; C65; clustering; social networks; power law distri- bution