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Title: Eigenvalue spectra of complex networks
Authors: Rodgers, GJ
Austin, K
Kahng, B
Kim, D
Issue Date: 2005
Publisher: Institute of Physics Publishing
Citation: Journal of Physics A: Mathematical and General, 38(43): 9431-9437(7), Oct 2005
Abstract: We examine the eigenvalue spectrum, (), of the adjacency matrix of a random scale-free network with an average of p edges per vertex using the replica method. We show how in the dense limit, when p , one can obtain two relatively simple coupled equations whose solution yields () for an arbitrary complex network. For scale-free graphs, with degree distribution exponent , we obtain an exact expression for the eigenvalue spectrum when = 3 and show that () ~ 1/2-1 for large . In the limit we recover known results for the Erdös–Rényi random graph.
Appears in Collections:Mathematical Physics
Dept of Mathematics Research Papers
Mathematical Sciences

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