中国物理B ›› 2025, Vol. 34 ›› Issue (1): 10202-010202.doi: 10.1088/1674-1056/ad8a47

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Self-similarity of multilayer networks

Bing Wang(王冰)1,2, Huizhi Yu(于蕙芷)1, and Daijun Wei(魏代俊)1,†   

  1. 1 School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, China;
    2 School of Management Science and Engineer, Dongbei University of Finance and Economics, Dalian 116025, China
  • 收稿日期:2024-07-19 修回日期:2024-09-13 接受日期:2024-10-23 发布日期:2025-01-02
  • 通讯作者: Daijun Wei E-mail:2001013@hbmzu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61763009 and 72172025).

Self-similarity of multilayer networks

Bing Wang(王冰)1,2, Huizhi Yu(于蕙芷)1, and Daijun Wei(魏代俊)1,†   

  1. 1 School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, China;
    2 School of Management Science and Engineer, Dongbei University of Finance and Economics, Dalian 116025, China
  • Received:2024-07-19 Revised:2024-09-13 Accepted:2024-10-23 Published:2025-01-02
  • Contact: Daijun Wei E-mail:2001013@hbmzu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61763009 and 72172025).

摘要: Research on the self-similarity of multilayer networks is scarce, when compared to the extensive research conducted on the dynamics of these networks. In this paper, we use entropy to determine the edge weights in each sub-network, and apply the degree-degree distance to unify the weight values of connecting edges between different sub-networks, and unify the edges with different meanings in the multilayer network numerically. At this time, the multilayer network is compressed into a single-layer network, also known as the aggregated network. Furthermore, the self-similarity of the multilayer network is represented by analyzing the self-similarity of the aggregate network. The study of self-similarity was conducted on two classical fractal networks and a real-world multilayer network. The results show that multilayer networks exhibit more pronounced self-similarity, and the intensity of self-similarity in multilayer networks can vary with the connection mode of sub-networks.

关键词: multilayer networks, self-similarity, degree-degree distance, entropy

Abstract: Research on the self-similarity of multilayer networks is scarce, when compared to the extensive research conducted on the dynamics of these networks. In this paper, we use entropy to determine the edge weights in each sub-network, and apply the degree-degree distance to unify the weight values of connecting edges between different sub-networks, and unify the edges with different meanings in the multilayer network numerically. At this time, the multilayer network is compressed into a single-layer network, also known as the aggregated network. Furthermore, the self-similarity of the multilayer network is represented by analyzing the self-similarity of the aggregate network. The study of self-similarity was conducted on two classical fractal networks and a real-world multilayer network. The results show that multilayer networks exhibit more pronounced self-similarity, and the intensity of self-similarity in multilayer networks can vary with the connection mode of sub-networks.

Key words: multilayer networks, self-similarity, degree-degree distance, entropy

中图分类号:  (Combinatorics; graph theory)

  • 02.10.Ox
89.75.Fb (Structures and organization in complex systems)