Motif-based communities in complex networks

By Alex Arenas, Alberto Fernández, Santo Fortunato, Sergio Gómez. 2007

137 citations recorded by the source corpus.

Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest neighbors, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman–Girvan modularity. We construct then a general framework and apply it to some synthetic and real networks.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fdbe3baeabdf8a10531393b87b14081e9b87e855

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In Computational Theory and Mathematics

In Computer Vision and Pattern Recognition

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Citations in the corpus

Synchronization in complex networks (2008, background): “…in terms of the adjacency matrix aij and the total number of links M = 1 2 ∑ i ki as Q = 1 2M ∑ ij (aij − kikj 2M )δci,cj (2) where ci is the community to which node i is assigned and the Kronecker delta function δci,cj takes the value 1 if nodes i and j are in the same community, and 0 otherwise.”
Communities in Networks (2009, methodology): “The notion of motifs has also recently been used to develop generalizations of graph modularity [5].”
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.”
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).”
Detecting communities of triangles in complex networks using spectral optimization (2010, background): “Triangle modularity tensor In [26] some of us introduced a mathematical formalism to cop e with modularity of motifs of any size.”
Community Structure in Graphs (2007, background): “A more general definition, where one counts small connected subgraphs (motifs), and not necessarily edges, can be found in [27].”