A change of perspective in network centrality

TL;DR

This paper introduces a new theoretical perspective on network centrality based on the adjacency matrix, revealing limitations of standard metrics and proposing more informative multi-component measures.

Contribution

It presents a natural, matrix-based framework for defining and comparing centrality measures, and introduces advanced multi-component metrics for complex networks.

Findings

Standard centrality metrics perform inadequately on complex networks

The proposed framework allows natural derivation of various centrality measures

Multi-component centrality metrics outperform traditional ones

Abstract

Typing Yesterday into the search-bar of your browser provides a long list of websites with, in top places, a link to a video by The Beatles. The order your browser shows its search results is a notable example of the use of network centrality. Centrality is a measure of the importance of the nodes in a network and it plays a crucial role in a huge number of fields, ranging from sociology to engineering, and from biology to economics. Many metrics are available to evaluate centrality. However, centrality measures are generally based on ad hoc assumptions, and there is no commonly accepted way to compare the effectiveness and reliability of different metrics. Here we propose a new perspective where centrality definition arises naturally from the most basic feature of a network, its adjacency matrix. Following this perspective, different centrality measures naturally emerge, including the degree, eigenvector, and hub-authority centrality. Within this theoretical framework, the accuracy of different metrics can be compared. Tests on a large set of networks show that the standard centrality metrics perform unsatisfactorily, highlighting intrinsic limitations of these metrics for describing the centrality of nodes in complex networks. More informative multi-component centrality metrics are proposed as the natural extension of standard metrics.