PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Spectra of Modular Random Graphs
Guler Ergun and Reimer Kuehn
Journal of Physics: Math-Gen Volume 42, 395001-(14pp), 2009.


We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete. Two different types of inter-module connectivity are considered, one where the number of intermodule connections per-node diverges, and one where this number remains finite in the infinite module-size limit. In the first case, results can be understood as a perturbation of a superposition of semicircular spectral densities one would obtain for uncoupled modules. In the second case, matters can be more involved, and depend in detail on inter-module connectivities. For suitable parameters we even find near-triangular shaped spectral densities, similar to those observed in certain scale-free networks, in a system of consisting of just two coupled modules. Analytic results are presented for the infinite module-size limit; they are well corroborated by numerical simulations.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:6310
Deposited By:Reimer Kuehn
Deposited On:08 March 2010