Small-world spectra in mean field theory

Details Small-world spectra in mean field theory Small-world spectra in mean field theory

2011-12-07

arxiv.org/abs/1112.1728v1

Physics

Physics and Society

5 pages, 4 figures

Scientific paper

Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering and social science.

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