The Rank of Random Graphs
Kevin P. Costello, Van H. Vu
Abstract
We show that almost surely the rank of the adjacency matrix of the Erdös-Rényi random graph G(n,p) equals the number of non-isolated vertices for any c 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.
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