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Random intersection graphs with tunable degree distribution and clustering
Stockholm University, Faculty of Science, Department of Mathematics.
2007 (English)Report (Other academic)
Abstract [en]

A random intersection graph is constructed by independently assigning 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 paper 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 determined 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 so 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.

Place, publisher, year, edition, pages
Matematiska institutionen, Stockholms universitet , 2007. , 16 p.
Series
Research reports in Mathematical Statistics, 2007:1
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-10201ISBN: 1650-0377 OAI: oai:DiVA.org:su-10201DiVA: diva2:176720
Available from: 2007-12-21 Created: 2007-12-21Bibliographically approved

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http://www.math.su.se/matstat/reports/seriea/2007/rep1/report.pdf
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