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Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Aug;70(2 Pt 2):025101. Epub 2004 Aug 19.

Modularity from fluctuations in random graphs and complex networks.

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Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.

Abstract

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to finding the ground-state energy of a spin system. Moreover, we demonstrate that, due to fluctuations, stochastic network models give rise to modular networks. Specifically, we show both numerically and analytically that random graphs and scale-free networks have modularity. We argue that this fact must be taken into consideration to define statistically significant modularity in complex networks.

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