Evaluation of node importance in complex networks

TL;DR

This paper introduces the Shannon-Parry measure (SPM) as a new, effective way to evaluate node importance in complex networks, demonstrating its accuracy and robustness across various network types.

Contribution

The paper proposes using SPM for node importance assessment, highlighting its effectiveness in weighted and directed networks, and validating it through multiple network analyses.

Findings

SPM outperforms existing methods in accuracy and robustness

SPM effectively analyzes weighted and directed networks

Application to China Railways High-speed network yields reasonable results

Abstract

The assessment of node importance has been a fundamental issue in the research of complex networks. In this paper, we propose to use the Shannon-Parry measure (SPM) to evaluate the importance of a node quantitatively, because SPM is the stationary distribution of the most unprejudiced random walk on the network. We demonstrate the accuracy and robustness of SPM compared with several popular methods in the Zachary karate club network and three toy networks. We apply SPM to analyze the city importance of China Railways High-speed (CRH) network, and obtain reasonable results. Since SPM can be used effectively in weighted and directed network, we believe it is a relevant method to identify key nodes in networks.