On the Laplacian Eigenvalues of Gn,p
2007 ◽
Vol 16
(6)
◽
pp. 923-946
◽
Keyword(s):
We investigate the Laplacian eigenvalues of sparse random graphs Gnp. 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 = Gnp 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(Gnp). 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 Gnp, their results imply that in the ‘dense’ case d ≥ ln2n the spectral gap of $\LL(\gnp)$ is 1-O (d−1/2) w.h.p.
Keyword(s):
2010 ◽
Vol 13
(4)
◽
pp. 403-412
◽
2006 ◽
Vol 29
(2)
◽
pp. 226-242
◽
Keyword(s):
2019 ◽
Vol 11
(2)
◽
pp. 407-417
◽