The vertex degree distribution of random intersection graphs

Authors:
Dudley Stark
Affiliations:
School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, United Kingdom
Venue:
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Year:
2004

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Abstract

Random intersection graphs are a model of random graphs in which each vertex is assigned a subset of a set of objects independently and two vertices are adjacent if their assigned subsets are not disjoint. The number of vertices is denoted by n and the number of objects is supposed to be ⌊nα⌋ for some α 0. We determine the distribution of the degree of a typical vertex and show that it changes sharply between α 1, α = 1, and α 1. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004