A Topological Centrality Measure for Directed Networks

TL;DR

This paper introduces a novel topological centrality measure called quasi-centrality for directed networks, capturing propagation dynamics and identifying influential nodes and sources of shocks using topological data analysis.

Contribution

It develops a new quasi-centrality measure for directed weighted networks and a hierarchical method to analyze topological influences, advancing network analysis beyond traditional measures.

Findings

Quasi-centrality effectively captures propagating effects in trade networks.

The measure identifies key sources of shocks disrupting network topology.

Hierarchical representation reveals topological influence of nodes.

Abstract

Given a directed network $ G $, we are interested in studying the qualitative features of $ G $ which govern how perturbations propagate across $ G $. Various classical centrality measures have been already developed and proven useful to capture qualitative features and behaviors for undirected networks. In this paper, we use topological data analysis (TDA) to adapt measures of centrality to capture both directedness and non-local propagating behaviors in networks. We introduce a new metric for computing centrality in directed weighted networks, namely the quasi-centrality measure. We compute these metrics on trade networks to illustrate that our measure successfully captures propagating effects in the network and can also be used to identify sources of shocks that can disrupt the topology of directed networks. Moreover, we introduce a method that gives a hierarchical representation of the topological influences of nodes in a directed network.