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- W2109286989 abstract "We investigate the Laplacian eigenvalues of sparse random graphs G np . We show that in the case that the expected degree d = ( n -1) p is bounded, the spectral gap of the normalized Laplacian $LL(gnp)$ is o (1). Nonetheless, w.h.p. G = G np has a large subgraph core(G) such that the spectral gap of $LL(core(G))$ is as large as 1- O ( d −1/2 ). We derive similar results regarding the spectrum of the combinatorial Laplacian L (G np ). The present paper complements the work of Chung, Lu and Vu [8] on the Laplacian spectra of random graphs with given expected degree sequences. Applied to G np , their results imply that in the ‘dense’ case d ≥ ln 2 n the spectral gap of $LL(gnp)$ is 1- O ( d −1/2 ) w.h.p." @default.
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- W2109286989 date "2007-11-01" @default.
- W2109286989 modified "2023-09-23" @default.
- W2109286989 title "On the Laplacian Eigenvalues of G<sub><i>n,p</i></sub>" @default.
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- W2109286989 doi "https://doi.org/10.1017/s0963548307008693" @default.
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