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The Vertex Degree Distribution of Passive Random Intersection Graph Models

Published online by Cambridge University Press:  01 July 2008

JERZY JAWORSKI  and
DUDLEY STARK
JERZY JAWORSKI
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland (e-mail: jaworski@amu.edu.pl)
DUDLEY STARK
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK (e-mail: D.S.Stark@maths.qmul.ac.uk)
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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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 4 , July 2008 , pp. 549 - 558
Copyright
Copyright © Cambridge University Press 2008

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References

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