Composite Centrality: A Natural Scale for Complex Evolving Networks

TL;DR

This paper introduces a unified composite centrality measure for complex networks, standardizing various measures into a normal distribution to compare node and edge importance across evolving systems.

Contribution

It develops a novel, invariant statistical framework for measuring centrality in weighted, directed networks, applicable to large, dynamic systems.

Findings

Effective in real-world networks like trade and migration webs

Achieves a normal distribution for composite centrality measures

Demonstrates high accuracy and normative power in complex systems

Abstract

We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures providing additional information, while the composite centrality measure tends to the standard normal distribution. This offers a unified scale to measure node and edge centralities for complex evolving networks under a uniform framework. Considering two real-world cases of the world trade web and the world migration web, both during a time span of 40 years, we propose a standard set-up to demonstrate its remarkable normative power and accuracy. We illustrate the applicability of the proposed framework for large and arbitrary complex systems, as well as its limitations, through extensive numerical simulations.