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http://bura.brunel.ac.uk/handle/2438/418
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/418 http://www.iop.org/EJ/journal/JPhysA/8 |
DOI: | http://dx.doi.org/10.1088/0305-4470/38/43/003 |
Appears in Collections: | Mathematical Physics Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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Eigenvalue.pdf | 356 kB | Adobe PDF | View/Open |
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