THe largest eigenvalue of sparse random graphs

Details THe largest eigenvalue of sparse random graphs THe largest eigenvalue of sparse random graphs

2001-06-10

arxiv.org/abs/math/0106066v1

Mathematics

Combinatorics

Scientific paper

We prove that for all values of the edge probability p(n) the largest
eigenvalue of a random graph G(n,p) satisfies almost surely:
\lambda_1(G)=(1+o(1))max{\sqrt{\Delta},np}, where \Delta is a maximal degree of
G, and the o(1) term tends to zero as max{\sqrt{\Delta},np} tends to infinity.

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