THe largest eigenvalue of sparse random graphs
Krivelevich, Michael · Sudakov, Benny
Original · EN
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: λ₁(G)=(1+o(1))max√Δ,np, where Δis a maximal degree of G, and the o(1) term tends to zero as max√Δ,np tends to infinity.
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