A new structure entropy of complex networks based on nonextensive statistical mechanics and similarity of nodes

Bing Wang; Fu Tan; Jia Zhu; Daijun Wei; Bing Wang; Fu Tan; Jia Zhu; Daijun Wei

doi:10.3934/mbe.2021187

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3718-3732. doi: 10.3934/mbe.2021187

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Research article

A new structure entropy of complex networks based on nonextensive statistical mechanics and similarity of nodes

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

Received: 25 February 2021 Accepted: 13 April 2021 Published: 29 April 2021

Entropy has been widely measured the complexity of complex networks. At present, many measures about entropies were defined based on the directed connection of nodes. The similarity of nodes can better represent the relationship among all nodes in complex networks. In the definition of similarity of nodes, the importance of a node in the network depends not only on the degree of the node itself, but also on the extent of dependence of neighboring nodes on the node. In this paper, we proposed a new structure entropy based on nonextensive statistical mechanics and similarity of nodes. In the proposed method, the similarity of nodes and the betweenness of nodes are both quantified. The proposed method considers the extent of dependence between neighbouring nodes. For some complex networks, the proposed structure entropy can distinguish complexity of that while other entropies can not be. Meanwhile, we construct five ER random networks and small-world networks and some real-world complex networks such as the US Air Lines networks, the GD'01-GD Proceedings Self-Citing networks, the Science Theory networks, the Centrality Literature networks and the Yeast networks are measured by the proposed method. The results illustrated our method for quantifying the complexity of complex networks is effective.
- complex network,
- structure entropy,
- similarity of nodes,
- nonextensive statistical mechanics,
- Tsallis entropy
Citation: Bing Wang, Fu Tan, Jia Zhu, Daijun Wei. A new structure entropy of complex networks based on nonextensive statistical mechanics and similarity of nodes[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3718-3732. doi: 10.3934/mbe.2021187

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Abstract

Entropy has been widely measured the complexity of complex networks. At present, many measures about entropies were defined based on the directed connection of nodes. The similarity of nodes can better represent the relationship among all nodes in complex networks. In the definition of similarity of nodes, the importance of a node in the network depends not only on the degree of the node itself, but also on the extent of dependence of neighboring nodes on the node. In this paper, we proposed a new structure entropy based on nonextensive statistical mechanics and similarity of nodes. In the proposed method, the similarity of nodes and the betweenness of nodes are both quantified. The proposed method considers the extent of dependence between neighbouring nodes. For some complex networks, the proposed structure entropy can distinguish complexity of that while other entropies can not be. Meanwhile, we construct five ER random networks and small-world networks and some real-world complex networks such as the US Air Lines networks, the GD'01-GD Proceedings Self-Citing networks, the Science Theory networks, the Centrality Literature networks and the Yeast networks are measured by the proposed method. The results illustrated our method for quantifying the complexity of complex networks is effective.

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