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An indicator for presence of community structure in networks is suggested. It allows one to check whether such structures can exist, in principle, in any particular network, without a need to apply computationally cost algorithms. In this way we exclude a large class of networks that do not possess any community structure.
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large number of mutua
Modern statistical modeling is an important complement to the more traditional approach of physics where Complex Systems are studied by means of extremely simple idealized models. The Minimum Description Length (MDL) is a principled approach to stati
Community structure is an important factor in the behavior of real-world networks because it strongly affects the stability and thus the phase transition order of the spreading dynamics. We here propose a reversible social contagion model of communit
Community identification of network components enables us to understand the mesoscale clustering structure of networks. A number of algorithms have been developed to determine the most likely community structures in networks. Such a probabilistic or
We present a new layout algorithm for complex networks that combines a multi-scale approach for community detection with a standard force-directed design. Since community detection is computationally cheap, we can exploit the multi-scale approach to