Self-similarity of multilayer networks

doi:10.1088/1674-1056/ad8a47

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.

Keywords: multilayer networks self-similarity degree-degree distance entropy

Received: 19 July 2024
Revised: 13 September 2024
Accepted manuscript online: 23 October 2024

PACS:	02.10.Ox	(Combinatorics; graph theory)
	89.75.Fb	(Structures and organization in complex systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61763009 and 72172025).

Corresponding Authors: Daijun Wei
E-mail: 2001013@hbmzu.edu.cn

Cite this article:

Bing Wang(王冰), Huizhi Yu(于蕙芷), and Daijun Wei(魏代俊) Self-similarity of multilayer networks 2025 Chin. Phys. B 34 010202

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