On Decay Centrality

TL;DR

This paper explores the relationship between decay centrality and two simpler measures, degree and closeness, revealing how decay parameter values influence which nodes are most central.

Contribution

It establishes theoretical links between decay centrality and degree/closeness, providing practical guidelines for approximating decay centrality in networks.

Findings

Nodes with maximum decay centrality align with maximum degree at low decay values.

Nodes with maximum decay centrality align with maximum closeness at high decay values.

A simple rule of thumb can nearly optimally approximate decay centrality with high probability.

Abstract

We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness. We show that for low values of the decay parameter the nodes with maximum decay centrality also have maximum degree, whereas for high values of the decay parameter they also maximize closeness. For intermediate values, we provide sufficient conditions that allow the comparison of decay centrality of different nodes and we show via numerical simulations that in the vast majority of networks, the nodes with maximum decay centrality are characterized by a threshold on the decay parameter below which they belong to the set of nodes with maximum degree and above which they belong to the set of nodes with maximum closeness. We also propose a simple rule of thumb that ensures a nearly optimal choice with very high probability.