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Vertex similarity is a major concept in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices (graph matching). With respect to the former problem, we propose to optimize a geometric objective that allows us to express each vertex uniquely as a convex combination of a few extreme types of vertices. Our method has the important advantage of supportingdoi:10.1080/15427951.2013.836581 fatcat:zbspo5l475ejzbfeijefzol34y