The Spectral Gap of Random Graphs with Given Expected Degrees
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We investigate the Laplacian eigenvalues of a random graph $G(n,\vec d)$ with a given expected degree distribution $\vec d$. The main result is that w.h.p. $G(n,\vec d)$ has a large subgraph core$(G(n,\vec d))$ such that the spectral gap of the normalized Laplacian of core$(G(n,\vec d))$ is $\geq1-c_0\bar d_{\min}^{-1/2}$ with high probability; here $c_0>0$ is a constant, and $\bar d_{\min}$ signifies the minimum expected degree. The result in particular applies to sparse graphs with $\bar d_{\min}=O(1)$ as $n\rightarrow\infty$. The present paper complements the work of Chung, Lu, and Vu [Internet Mathematics 1, 2003].
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2007 ◽
Vol 16
(6)
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pp. 923-946
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2016 ◽
Vol 113
(44)
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pp. 12368-12373
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2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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2015 ◽
Vol 25
(3)
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pp. 436-447
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