Identifying vital nodes in complex networks by adjacency information entropy

Xiang Xu,Qingyong Wang,Xianqiang Zhu,Cheng Zhu,Yun Zhou

doi:10.1038/s41598-020-59616-w

Xiang Xu, Qingyong Wang + Show 3 more

Open Access

https://doi.org/10.1038/s41598-020-59616-w

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Journal: Scientific Reports	Publication Date: Feb 14, 2020
Citations: 34	License type: open-access

Affiliation: National University of Defense Technology

Abstract

Identifying the vital nodes in networks is of great significance for understanding the function of nodes and the nature of networks. Many centrality indices, such as betweenness centrality (BC), eccentricity centrality (EC), closeness centricity (CC), structural holes (SH), degree centrality (DC), PageRank (PR) and eigenvector centrality (VC), have been proposed to identify the influential nodes of networks. However, some of these indices have limited application scopes. EC and CC are generally only applicable to undirected networks, while PR and VC are generally used for directed networks. To design a more applicable centrality measure, two vital node identification algorithms based on node adjacency information entropy are proposed in this paper. To validate the effectiveness and applicability of the proposed algorithms, contrast experiments are conducted with the BC, EC, CC, SH, DC, PR and VC indices in different kinds of networks. The results show that the index in this paper has a high correlation with the local metric DC, and it also has a certain correlation with the PR and VC indices for directed networks. In addition, the experimental results indicate that our algorithms can effectively identify the vital nodes in different networks.

Highlights

Identifying the vital nodes in networks is of great significance for understanding the function of nodes and the nature of networks
In the paper by Yu et al.[13], an improved method called improved structural holes (ISH) that identifies the key nodes in complex networks was proposed; unlike the eccentricity and betweenness centrality, this method can be applied to large-scale and disconnected networks
With respect to the unweighted-undirected networks, the Astro network is a collaboration network of astrophysics scientists[28]; the CA network is a large connected component of the arXiv collaboration network in high-energy physics theory[29]; the Facebook network is an anonymised social networks with 4039 users, where the data can be downloaded in http://snap.stanford.edu/ data/; and the Hamster network is a friendship and family connections network among website users[30]

Summary

Introduction

Identifying the vital nodes in networks is of great significance for understanding the function of nodes and the nature of networks. We study vital node identification in four different types of networks, namely, unweighted-undirected networks, unweighted-directed networks, weighted-undirected networks and weighted-directed networks. The degree of nodes in unweighted-undirected networks can be calculated by ki = ∑mj=1aij, where j is the neighbour of node i and m is the number of neighbours of node i.

Results

Conclusion