Small-world network spectra in mean-field theory

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...

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Bibliographic Details
Published in:Physical review letters 2012-05, Vol.108 (21), p.218701-218701, Article 218701
Main Authors: Grabow, Carsten, Grosskinsky, Stefan, Timme, Marc
Format: Article
Language:English
Subjects:
Models, Theoretical
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.108.218701