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Title: Assessing segregation in complex networks through a multifocal approach Authors:  Madalina Olteanu - Pantheon-Sorbonne University (France)
Julien Randon-Furling - Universite Paris 1 Pantheon Sorbonne (France) [presenting]
Abstract: The issue of revealing and quantifying multiscalar patterns of segregation in complex social networks is addressed. Instead of clustering or detecting communities, our new method provides a multifocal image of the network while highlighting its most segregated zones, its hotspots in terms of segregation. Inspired by a previous work with spatial data, we consider a connected graph with weighted edges, weights representing distances (spatial, social, ). Each vertex in the graph carries the value taken by a random variable. The empirical probability distribution in the whole network is known. To each vertex, we sequentially aggregate its neighbours according to a shortest path rule and/or a random walk. For each aggregated group, the probability distribution within the group is compared to that of the entire network. Eventually, for each of these trajectories of aggregates, the distance converge to zero, but the way this is achieved encompasses all information on the relative singularity of the starting vertex within the network. Furthermore, by comparing the actual trajectories with those obtained from random permutations of the vertex values, one may characterize the global structure of the network and its global level of segregation.