Analyzing complex networks through correlations in centrality measurements

TL;DR

This paper investigates how different centrality measures in complex networks are correlated across real and model networks, proposing a correlation profile to characterize and compare network structures.

Contribution

It introduces the concept of a centrality correlation profile to characterize networks and assesses its effectiveness using real and model networks, including biological data.

Findings

Centralities are generally correlated, more so in network models.

Correlation strength varies across different real networks.

The correlation profile can evaluate network model adequacy.

Abstract

Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some centrality measures, with different centrality definitions stressing different aspects of the network. It is interesting to know to what extent these different centrality definitions are related for different networks. In this work, we study the correlation between pairs of a set of centrality measures for different real world networks and two network models. We show that the centralities are in general correlated, but with stronger correlations for network models than for real networks. We also show that the strength of the correlation of each pair of centralities varies from network to network. Taking this fact into account, we propose the use of a centrality correlation profile, consisting of the values of the correlation coefficients between all pairs of centralities of interest, as a way to characterize networks. Using the yeast protein interaction network as an example we show also that the centrality correlation profile can be used to assess the adequacy of a network model as a representation of a given real network.