The Spectral Gap of Random Graphs with Given Expected Degrees

  • Amin Coja-Oghlan
  • André Lanka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


We investigate the Laplacian eigenvalues of a random graph G(n,d) with a given expected degree distribution d. The main result is that w.h.p. G(n,d) has a large subgraph core(G(n,d)) such that the spectral gap of the normalized Laplacian of core(G(n,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. This result is of interest in order to extend known spectral heuristics for random regular graphs to graphs with irregular degree distributions, e.g., power laws. The present paper complements the work of Chung, Lu, and Vu [Internet Mathematics 1, 2003].


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Amin Coja-Oghlan
    • 1
  • André Lanka
    • 2
  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Fakultät für InformatikTechnische Universität ChemnitzChemnitzGermany

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