An entropy-based, scale-dependent centrality

TL;DR

This paper introduces a novel entropy-based, scale-dependent centrality measure for networks, which adapts to different scales by varying a parameter and unifies several classical centralities within a single framework.

Contribution

It proposes a new centrality measure based on Shannon entropy of a continuous-time random walk, capturing various known centralities as special cases depending on the scale parameter.

Findings

The new centrality effectively captures degree, eigenvector, and closeness centralities.

It provides a unified framework for total $f$-communicability centralities.

The measure adapts to different network scales through the parameter t.

Abstract

In this article we introduce an entropy-based, scale-dependent centrality that is evaluated as the Shannon entropy of the distribution at time t of a continuous-time random walk. It ranks nodes as a function of the time t, which acts as a parameter and defines the scale of the network. It is able capture well-known centralities such as degree, eigenvector and closeness depending on the range of t. We compare it with the broad class of total $f$-communicability centralities, of which both Katz centrality and total communicability are particular cases.