The rank of random graphs
Copyright policy )The rank of random graphs
AbstractWe show that almost surely the rank of the adjacency matrix of the Erdős‐Rényi random graph G(n,p) equals the number of nonisolated vertices for any c ln n/n ≤ p ≤ 1/2, where c is an arbitrary positive constant larger than 1/2. In particular, the adjacency matrix of the giant component (a.s.) has full rank in this range. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008
- Institute for Advanced Study United States
Graphs and linear algebra (matrices, eigenvalues, etc.), Littlewood-Offord, Probability (math.PR), Random graphs (graph-theoretic aspects), FOS: Mathematics, random matrix, Mathematics - Combinatorics, 15A52, Combinatorics (math.CO), Mathematics - Probability, random graph
Graphs and linear algebra (matrices, eigenvalues, etc.), Littlewood-Offord, Probability (math.PR), Random graphs (graph-theoretic aspects), FOS: Mathematics, random matrix, Mathematics - Combinatorics, 15A52, Combinatorics (math.CO), Mathematics - Probability, random graph
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