The vertex degree distribution of passive random intersection graph models

Authors:
Jerzy Jaworski;Dudley Stark
Affiliations:
Faculty of mathematics and computer science, adam mickiewicz university, ul. umultowska 87, 61-614 poznań, poland (e-mail: jaworski@amu.edu.pl);School of mathematical sciences, queen mary, university of london, london e1 4ns, uk (e-mail: d.s.stark@maths.qmul.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
2008

Citing 3
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Abstract

In a random passive intersection graph model the edges of the graph are decided by taking the union of a fixed number of cliques of random size. We give conditions for a random passive intersection graph model to have a limiting vertex degree distribution, in particular to have a Poisson limiting vertex degree distribution. We give related conditions which, in addition to implying a limiting vertex degree distribution, imply convergence of expectation.