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The spectral gap of random graphs with given expected degrees

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Coja-Oghlan, Amin and Lanka, André (2009) The spectral gap of random graphs with given expected degrees. Electronic Journal of Combinatorics, Vol.16 (No.1). R138. ISSN 1077-8926.

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Abstract

We investigate the Laplacian eigenvalues of a random graph G(n,d⃗ ) with a given expected degree distribution d⃗ . The main result is that w.h.p. G(n,d⃗ ) has a large subgraph core(G(n,d⃗ )) such that the spectral gap of the normalized Laplacian of core(G(n,d⃗ )) is ≥1−c0dˉ−1/2min with high probability; here c0>0 is a constant, and dˉmin signifies the minimum expected degree. The result in particular applies to sparse graphs with dˉmin=O(1) as n→∞. The present paper complements the work of Chung, Lu, and Vu [Internet Mathematics 1, 2003].

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Electronic Journal of Combinatorics
Publisher: Electronic Journal of Combinatorics
ISSN: 1077-8926
Official Date: 2009
Dates:
DateEvent
2009Published
Volume: Vol.16
Number: No.1
Page Range: R138
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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