The Rank of Random Graphs

Details The Rank of Random Graphs The Rank of Random Graphs

2006-06-17

arxiv.org/abs/math/0606414v1

Mathematics

Probability

19 pages, no figures

Scientific paper

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/nlarger than 1/2. In particular, the giant component (a.s.) has full rank in
this range.

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