Centrality Measures in Interval-Weighted Networks

TL;DR

This paper introduces a methodology to generalize key centrality measures for interval-weighted networks, accounting for edge weight variability, and applies it to real-world transportation and trade networks.

Contribution

It proposes a novel approach to extend degree, closeness, and betweenness centralities for networks with interval-valued edge weights, addressing a gap in existing methods.

Findings

Effective in analyzing real-world networks with uncertain edge weights

Provides insights into the importance of nodes in transportation and trade networks

Enhances understanding of network centrality under weight variability

Abstract

Centrality measures are used in network science to evaluate the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality, and betweenness centrality have solely assumed the edge weights to be constants. This paper proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (Interval-Weighted Networks -- IWN). We apply our centrality measures approach to two real-world IWN. The first is a commuter network in mainland Portugal, between the 23 NUTS 3 Regions. The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015.