Centralities in complex networks

TL;DR

This paper introduces various network centrality measures based on traversal concepts, providing an overview of their role in identifying important nodes in complex systems modeled as graphs.

Contribution

It offers an introductory overview of centrality measures in network science, focusing on traversal-based methods, and highlights their importance in analyzing complex networks.

Findings

Centrality measures help identify key nodes in networks.

Traversal-based centralities are fundamental in understanding network dynamics.

The paper provides an accessible overview of the topic.

Abstract

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant advances in the understanding of the structure, formation and function of complex systems. Social and biological processes such as the dynamics of epidemics, the diffusion of information in social media, the interactions between species in ecosystems or the communication between neurons in our brains are all actively studied using dynamical models on complex networks. In all of these systems, the patterns of connections at the individual level play a fundamental role on the global dynamics and finding the most important nodes allows one to better understand and predict their behaviors. An important research effort in network science has therefore been dedicated to the development of methods allowing to find the most important nodes in networks. In this short entry, we describe network centrality measures based on the notions of network traversal they rely on. This entry aims at being an introduction to this extremely vast topic, with many contributions from several fields, and is by no means an exhaustive review of all the literature about network centralities.