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|Title:||Eigenvalue spectra of complex networks|
|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
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