Abstract
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.
Highlights
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
We extend the standard definitions of these three metrics to embed the intrinsic relevance of vertices, showing that this information can increase the capability of centrality tools to assess the relevance of vertices and edges
About the function f(Rs,Rt), we argue that its structure is problem-dependent and the selection of a specific function allows to embed a diverse exogenous information in the standard centrality metrics
Summary
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. 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. Infrastructure networks (e.g., water and energy distribution networks) are another example of the importance to consider the intrinsic relevance of vertices In these cases, some strategic vertices, e.g., energy/water sources, hospitals, schools, administrative buildings, are characterized by a relevance independent from their topological position and connectivity; the intrinsic relevance needs to be embedded in the centrality evaluation to make useful CNT for such networked systems. We can state the identical intrinsic relevance of vertices is an inherent assumption CNT tools and that such assumption can hide a part of the network information, not allowing an effective analysis when vertices exhibit the heterogeneous intrinsic relevance
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