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Some New Properties for Degree-Based Graph Entropies

by Guoxiang Lu 1,2,3,*, Bingqing Li 2 and Lijia Wang 2
1
School of Economics, Nankai University, No. 94 Weijin Road, Tianjin 300071, China
2
School of Finance, Nankai University, No. 94 Weijin Road, Tianjin 300071, China
3
School of Statistics and Mathematics, Zhongnan University of Economics and Law, No. 182 Nanhu Avenue, Wuhan 430073, China
*
Author to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Entropy 2015, 17(12), 8217-8227; https://doi.org/10.3390/e17127871
Received: 21 October 2015 / Revised: 4 December 2015 / Accepted: 10 December 2015 / Published: 16 December 2015
(This article belongs to the Section Complexity)
The graph entropies inspired by Shannon’s entropy concept become the information-theoretic quantities for measuring the structural information of graphs and complex networks. In this paper, we continue studying some new properties of the graph entropies based on information functionals involving vertex degrees. We prove the monotonicity of the graph entropies with respect to the power exponent. Considering only the maximum and minimum degrees of the ( n , m ) -graph, we obtain some upper and lower bounds for the degree-based graph entropy. These bounds have different performances to restrict the degree-based graph entropy in different kinds of graphs. Moreover the degree-based graph entropy can be estimated by these bounds. View Full-Text
Keywords: Shannon’s entropy; graph entropy; degree powers; monotonicity; entropy bounds Shannon’s entropy; graph entropy; degree powers; monotonicity; entropy bounds
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Lu, G.; Li, B.; Wang, L. Some New Properties for Degree-Based Graph Entropies. Entropy 2015, 17, 8217-8227.

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