The phase transition in inhomogeneous random intersection graphs
Discrete Mathematics
2013-01-31 v1 Combinatorics
Probability
Abstract
We analyze the component evolution in inhomogeneous random intersection graphs when the average degree is close to 1. As the average degree increases, the size of the largest component in the random intersection graph goes through a phase transition. We give bounds on the size of the largest components before and after this transition. We also prove that the largest component after the transition is unique. These results are similar to the phase transition in Erd\H{o}s-R\'enyi random graphs; one notable difference is that the jump in the size of the largest component varies in size depending on the parameters of the random intersection graph.
Keywords
Cite
@article{arxiv.1301.7320,
title = {The phase transition in inhomogeneous random intersection graphs},
author = {Milan Bradonjić and Aric Hagberg and Nicolas W. Hengartner and Nathan Lemons and Allon G. Percus},
journal= {arXiv preprint arXiv:1301.7320},
year = {2013}
}
Comments
18 pages