Analysis of the structure of complex networks at different resolution levels

By Alex Arenas, Alberto Fernández, Sergio Gómez. 2007

556 citations recorded by the source corpus.

Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights into the structure–functionality relationship. The standard approach is based on the optimization of a quality function, modularity, which is a relative quality measure for the partition of a network into modules. Recently, some authors (Fortunato and Barthélemy 2007 Proc. Natl Acad. Sci. USA 104 36 and Kumpula et al 2007 Eur. Phys. J. B 56 41) have pointed out that the optimization of modularity has a fundamental drawback: the existence of a resolution limit beyond which no modular structure can be detected even though these modules might have their own entity. The reason is that several topological descriptions of the network coexist at different scales, which is, in general, a fingerprint of complex systems. Here, we propose a method that allows for multiple resolution screening of the modular structure. The method has been validated using synthetic networks, discovering the predefined structures at all scales. Its application to two real social networks allows us to find the exact splits reported in the literature, as well as the substructure beyond the actual split.

Subfields: Cognitive Neuroscience, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/196ce11e9540e853eb2e7dd7c11408d4e5a1359d

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Citations in the corpus

Communities in Networks (2009, background): “parameter [6, 104] that allows one to examine”
Community detection in networks: A user guide (2016, methodology): “Indeed, one could formulate the network clustering problem by focusing on higher order structures, like motifs (e. g., triangles) (Arenas et al., 2008a; Benson et al., 2016; Serrour et al., 2011).”
Open Community Challenge Reveals Molecular Network Modules with Key Roles in Diseases (2018, methodology): “, 2001); the runner-up team (M1) extended different modularity optimization methods with a resistance parameter that controls the granularity of modules (Arenas et al., 2008); and the third-ranking team (R1) used a random-walk method based on multi-level”
On the permanence of vertices in network communities (2014, background): “To address these issues, multi-resolution versions of modularity [2] were proposed to allow researchers to specify a tunable target resolution limit parameter.”
Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks (2008, background): “cance of a particular partition based on its robustness in three different ways [73], [74], [75], [76], [77], [78]: (i) robust (persistent) across time; (ii) robust to small perturbations to the graph; and (iii) robust to the optimization algorithm and the starting point of the optimization.”
Comparing Community Structure to Characteristics in Online Collegiate Social Networks (2008, background): “Meanwhile, the observed heterogeneity in the communities, even at an institution like Caltech whose social structure seems to be mostly dominated by a single feature (House affiliation), underscores the important point that networks typically have multiple levels of organization rather than a single”
Communities, modules and large-scale structure in networks (2011, unknown): “Modifications of the method have been proposed that allow one to vary this preferred size 59,60 , but not to eliminate the preference altogether.”
Community detection in graphs (2009, methodology): “Interestingly, Arenas et al. found that the structural scales revealed by synchronization correspond to groups of eigenvalues of the Laplacian matrix of the graph, separated by gaps (Fig.”
Modular Brain Networks (2015, methodology): “To circumvent the resolution limit issue, a number of multiresolution techniques have been proposed (Arenas et al. 2008, Reichardt & Bornholdt 2006).”