Centers of complex networks

The central vertices in complex networks are of particular interest because they might play the role of organizational hubs. Here, we consider three different geometric centrality measures, excentricity, status, and centroid value, that were originally used in the context of resource placement problems. We show that these quantities lead to useful descriptions of the centers of biological networks which often, but not always, correlate with a purely local notion of centrality such as the vertex degree. We introduce the notion of local centers as local optima of a centrality value “landscape” on a network and discuss briefly their role.