A new structural entropy measurement of networks based on the nonextensive statistical mechanics and hub repulsion

Fu Tan; Bing Wang; Daijun Wei; Fu Tan; Bing Wang; Daijun Wei

doi:10.3934/mbe.2021455

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 9253-9263. doi: 10.3934/mbe.2021455

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Research article

A new structural entropy measurement of networks based on the nonextensive statistical mechanics and hub repulsion

Department of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, China

Academic Editor: Congping Lin

Received: 16 August 2021 Accepted: 18 October 2021 Published: 26 October 2021

The structure properties of complex networks are an open issue. As the most important parameter to describe the structural properties of the complex network, the structure entropy has attracted much attention. Recently, the researchers note that hub repulsion plays an role in structural entropy. In this paper, the repulsion between nodes in complex networks is simulated when calculating the structure entropy of the complex network. Coulomb's law is used to quantitatively express the repulsive force between two nodes of the complex network, and a new structural entropy based on the Tsallis nonextensive statistical mechanics is proposed. The new structure entropy synthesizes the influence of repulsive force and betweenness. We study several construction networks and some real complex networks, the results show that the proposed structure entropy can describe the structural properties of complex networks more reasonably. In particular, the new structural entropy has better discrimination in describing the complexity of the irregular network. Because in the irregular network, the difference of the new structure entropy is larger than that of degree structure entropy, betweenness structure entropy and Zhang's structure entropy. It shows that the new method has better discrimination for irregular networks, and experiments on Graph, Centrality literature, US Aire lines and Yeast networks confirm this conclusion.
- complex networks,
- structure entropy,
- coulomb's law,
- tsallis nonextensive statistical mechanics
Citation: Fu Tan, Bing Wang, Daijun Wei. A new structural entropy measurement of networks based on the nonextensive statistical mechanics and hub repulsion[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 9253-9263. doi: 10.3934/mbe.2021455

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Abstract

The structure properties of complex networks are an open issue. As the most important parameter to describe the structural properties of the complex network, the structure entropy has attracted much attention. Recently, the researchers note that hub repulsion plays an role in structural entropy. In this paper, the repulsion between nodes in complex networks is simulated when calculating the structure entropy of the complex network. Coulomb's law is used to quantitatively express the repulsive force between two nodes of the complex network, and a new structural entropy based on the Tsallis nonextensive statistical mechanics is proposed. The new structure entropy synthesizes the influence of repulsive force and betweenness. We study several construction networks and some real complex networks, the results show that the proposed structure entropy can describe the structural properties of complex networks more reasonably. In particular, the new structural entropy has better discrimination in describing the complexity of the irregular network. Because in the irregular network, the difference of the new structure entropy is larger than that of degree structure entropy, betweenness structure entropy and Zhang's structure entropy. It shows that the new method has better discrimination for irregular networks, and experiments on Graph, Centrality literature, US Aire lines and Yeast networks confirm this conclusion.

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