Some New Properties for Degree-Based Graph Entropies

Entropy

Guoxiang Lu²  Bingqing Li¹  Lijia Wang¹ 

[1] School of Finance, Nankai University, No. 94 Weijin Road, Tianjin 300071, China;;School of Economics, Nankai University, No. 94 Weijin Road, Tianjin 300071, China

关键词: Shannon’s entropy;    graph entropy;    degree powers;    monotonicity;    entropy bounds;   

DOI  :  10.3390/e17127871

来源: mdpi

【 摘 要 】

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 -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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.