Interplay Between Hierarchy and Centrality in Complex Networks

TL;DR

This paper explores the relationship between hierarchy and centrality in complex networks, analyzing how different measures correlate across diverse real-world networks to understand their interplay.

Contribution

It systematically evaluates the correlation between multiple centrality and hierarchy measures across various networks, revealing the influence of network density and transitivity.

Findings

Network density affects centrality-hierarchy relationships

Transitivity influences measure correlations

Different networks show diverse measure interactions

Abstract

Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic allowing to identify key constituents. Several measures based on various aspects of network topology have been proposed in order to quantify these concepts. While numerous studies have investigated whether centrality measures convey redundant information, how centrality and hierarchy measures are related is still an open issue. In this paper, we investigate the interaction between centrality and hierarchy using several correlation and similarity evaluation measures. A series of experiments is performed in order to evaluate the combinations of 6 centrality measures with 4 hierarchy measures across 28 diverse real-world networks with varying topological characteristics. Results show that network density and transitivity play a key role in shaping the pattern of relations between centrality and hierarchy measures.