Abstract
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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Coja-Oghlan, A., Lanka, A. (2006). The Spectral Gap of Random Graphs with Given Expected Degrees. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_3
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DOI: https://doi.org/10.1007/11786986_3
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