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Title: Local assortativity in weighted and directed complex networks Authors:  Marc Sabek - University of Wuppertal (Germany) [presenting]
Uta Pigorsch - University of Wuppertal (Germany)
Abstract: Assortativity measures the tendency of a vertex to bond with another based on similarity. It is commonly defined as the correlation coefficient between the excess degrees of both ends of an edge and is often associated with the robustness of a network against exogenous shocks. In this context, it is interesting to know which of the vertices or edges of a network are the most endangering on the one hand, and which are the most protective on the other hand. The assortativity coefficient, being a global measure, however, cannot provide answers to those kinds of questions. There is a need for a local assortativity measure, which can be either vertex or edge-based, in order to identify those vertices or edges that contribute most to the global assortativity structure of a network, respectively. Many real-world networks are weighted networks; however, local assortativity has been exclusively considered for unweighted networks, so far. By generalizing this concept to weighted and (un)directed networks, we unify two approaches used in the literature, and derive distinct measures that allow us to determine the assortativeness of individual edges and vertices as well as of entire components of a weighted network. We demonstrate the usefulness of our measures by applying them to theoretical and real-world networks. Along this way, we also explain how to compute local assortativity profiles, which are informative about the pattern of local assortativity with respect to edge weight.