The Rank of Random Graphs

Kevin P. Costello; Van H. Vu

The Rank of Random Graphs

Probability 2007-05-23 v1 Combinatorics

Authors: Kevin P. Costello , Van H. Vu

Abstract

We show that almost surely the rank of the adjacency matrix of the Erd\"os-R\'enyi random graph $G(n,p)$ equals the number of non-isolated vertices for any $c\ln n/n<p<1/2$ , where $c$ is an arbitrary positive constant larger than 1/2. In particular, the giant component (a.s.) has full rank in this range.

Keywords

random graphs matrix rank preferential attachment

Cite

@article{arxiv.math/0606414,
  title  = {The Rank of Random Graphs},
  author = {Kevin P. Costello and Van H. Vu},
  journal= {arXiv preprint arXiv:math/0606414},
  year   = {2007}
}

Comments

19 pages, no figures

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