Embedding the intrinsic relevance of vertices in network analysis: the case of centrality metrics

Complex network theory (CNT) is gaining a lot of attention in the scientific community, due to its capability to model and interpret an impressive number of natural and anthropic phenomena. One of the most active CNT field concerns the evaluation of the centrality of vertices and edges in the network. Several metrics have been proposed, but all of them share a topological point of view, namely centrality descends from the local or global connectivity structure of the network. However, vertices can exhibit their own intrinsic relevance independent from topology; e.g., vertices representing strategic locations (e.g., hospitals, water and energy sources, etc.) or institutional roles (e.g., presidents, agencies, etc.). In these cases, the connectivity network structure and vertex intrinsic relevance mutually concur to define the centrality of vertices and edges. The purpose of this work is to embed the information about the intrinsic relevance of vertices into CNT tools to enhance the network analysis. We focus on the degree, closeness and betweenness metrics, being among the most used. Two examples, concerning a social (the historical Florence family's marriage network) and an infrastructure (a water supply system) network, demonstrate the effectiveness of the proposed relevance-embedding extension of the centrality metrics.