Spectral density of random graphs with topological constraints

Details Spectral density of random graphs with topological constraints Spectral density of random graphs with topological constraints

2009-10-19

arxiv.org/abs/0910.3556v2

J. Phys. A: Math. Theor. 43 195002, 2010

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages, 6 figures

Scientific paper

10.1088/1751-8113/43/19/195002

The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case an exact solution is found for the spectral density in the form of consistency equations depending on the statistical properties of the graph ensemble in question. We highlight the effect of these topological constraints on the resulting spectral density.

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