Nodes and layers PageRank centrality for multilayer networks

doi:10.1088/1674-1056/28/2/020501

中国物理B ›› 2019, Vol. 28 ›› Issue (2): 20501-020501.doi: 10.1088/1674-1056/28/2/020501

Nodes and layers PageRank centrality for multilayer networks

Lai-Shui Lv(吕来水), Kun Zhang(张琨), Ting Zhang(张婷), Meng-Yue Ma(麻孟越)

Nanjing University of Science and Technology, Nanjing 210094, China

收稿日期:2018-09-20 修回日期:2018-11-11 出版日期:2019-02-05 发布日期:2019-02-05
通讯作者: Kun Zhang E-mail:zhangkun@njust.edu.cn
基金资助:
Project supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. AE91313/001/016), the National Natural Science Foundation of China (Grant No. 11701097), and the Natural Science Foundation of Jiangxi Province, China (Grant No. 20161BAB212055).

Nodes and layers PageRank centrality for multilayer networks

Lai-Shui Lv(吕来水), Kun Zhang(张琨), Ting Zhang(张婷), Meng-Yue Ma(麻孟越)

Nanjing University of Science and Technology, Nanjing 210094, China

Received:2018-09-20 Revised:2018-11-11 Online:2019-02-05 Published:2019-02-05
Contact: Kun Zhang E-mail:zhangkun@njust.edu.cn
Supported by:
Project supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. AE91313/001/016), the National Natural Science Foundation of China (Grant No. 11701097), and the Natural Science Foundation of Jiangxi Province, China (Grant No. 20161BAB212055).

摘要/Abstract

摘要： In this paper, we propose a new centrality algorithm that can simultaneously rank the nodes and layers of multilayer networks, referred to as the MRFNL centrality. The centrality of nodes and layers are obtained by developing a novel iterative algorithm for computing a set of tensor equations. Under some conditions, the existence and uniqueness of this centrality were proven by applying the Brouwer fixed point theorem. Furthermore, the convergence of the proposed iterative algorithm was established. Finally, numerical experiments on a simple multilayer network and two real-world multilayer networks (i.e., Pierre Auger Collaboration and European Air Transportation Networks) are proposed to illustrate the effectiveness of the proposed algorithm and to compare it to other existing centrality measures.

关键词: multilayer networks, PageRank centrality, random walks, transition probability tensors

Abstract: In this paper, we propose a new centrality algorithm that can simultaneously rank the nodes and layers of multilayer networks, referred to as the MRFNL centrality. The centrality of nodes and layers are obtained by developing a novel iterative algorithm for computing a set of tensor equations. Under some conditions, the existence and uniqueness of this centrality were proven by applying the Brouwer fixed point theorem. Furthermore, the convergence of the proposed iterative algorithm was established. Finally, numerical experiments on a simple multilayer network and two real-world multilayer networks (i.e., Pierre Auger Collaboration and European Air Transportation Networks) are proposed to illustrate the effectiveness of the proposed algorithm and to compare it to other existing centrality measures.

Key words: multilayer networks, PageRank centrality, random walks, transition probability tensors

中图分类号: (Random walks and Levy flights)

05.40.Fb

89.75.Hc (Networks and genealogical trees) 89.75.-k (Complex systems)

吕来水, 张琨, 张婷, 麻孟越. Nodes and layers PageRank centrality for multilayer networks[J]. 中国物理B, 2019, 28(2): 20501-020501.

Lai-Shui Lv(吕来水), Kun Zhang(张琨), Ting Zhang(张婷), Meng-Yue Ma(麻孟越). Nodes and layers PageRank centrality for multilayer networks[J]. Chin. Phys. B, 2019, 28(2): 20501-020501.

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Nodes and layers PageRank centrality for multilayer networks

Nodes and layers PageRank centrality for multilayer networks

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