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

Orazio Giustolisi, Luca Ridolfi and Antonietta Simone

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.