Spectra of random graphs with given expected degrees

By Fan Chung, Linyuan Lu, Van H. Vu. Proceedings of the National Academy of Sciences of the United States of America, 2003

288 citations recorded by the source corpus.

How researchers see this paper

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Concentration Inequalities and Martingale Inequalities: A Survey (2006, background): “Indeed, many of these inequalities have been included in our previous papers [9, 10, 11, 12].”
A new space for comparing graphs (2014, background): “It is known that there is sharp concentration of eigenvalues of adjacency matrix A for random graphs [5].”
Synchronization in complex networks (2008, background): “So far studies on detailed spectral properties are still mainly restricted to random networks [123, 265, 266, 145, 267, 112] and only a few deal on the relation between synchronization patterns and spectral properties, out of the complete synchronization, see e.”
Spectra of Large Random Trees (2009, result): “These results extend and sharpen those in [19, 20, 24, 25], where it was shown that the k largest eigenvalues are asymptotically equivalent to the square roots of the k largest outdegrees.”
Distribution of shortest path lengths in subcritical Erdős-Rényi networks. (2018, background): “It will also be interesting to apply the topological expansion to edge-independent, inhomogeneous random graphs [17,62,63].”