Modularity from fluctuations in random graphs and complex networks.

By Roger Guimerà, Marta Sales-Pardo, Luís A. Nunes Amaral. Physical review. E, Statistical, nonlinear, and soft matter physics, 2004

867 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/974bf5024e445a9c5b140a2558a0e494e27223ec

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Citations in the corpus

Finding Statistically Significant Communities in Networks (2010, neutral): “value of variables estimated on the null model, neglecting random fluctuations, which is why modularity can attain large values on specific partitions of random graphs”
Robustness of community structure in networks. (2007, background): “Several authors have suggested that instead we should look for divisions of a network that have significantly higher modularity than the random graph [25, 26].”
Redrawing the Map of Great Britain from a Network of Human Interactions (2010, background): “58, indicative of a good partitioning compared to the randomized network, as mentioned in [15,20].”
The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database (2022, positive): “Besides, for a given proteome, the average fractal dimen-sion of the proteins can also be estimated by the size dependence of the modularity Q of the proteins’ residue contact networks (Guimerà et al. 2004; Tang and Kaneko 2020).”
Clustering and Community Detection in Directed Networks: A Survey (2013, neutral): “[46, 47]) and extremal optimization [48].”
Community detection in networks: A user guide (2016, background): “For one thing, there are highmodularity partitions even in random graphs without groups (Guimerà et al., 2004).”