A Note on Distance-based Graph Entropies

Entropy

Zengqiang Chen¹  Matthias Dehmer² 

[1] College of Computer and Control Engineering, Nankai University, No. 94 Weijin Road, 300071 Tianjin, China; E-Mail:;Department of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany; E-Mail:

关键词: entropy;    Shannon’s entropy;    graph entropy;    distance;    networks;   

DOI  :  10.3390/e16105416

来源: mdpi

【 摘 要 】

A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties such as a meaningful structural interpretation and uniqueness. As classical work, many distance-based graph entropies, e.g., the ones due to Bonchev et al. and related quantities have been proposed and studied. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices with distance k to a given vertex. In particular, we investigate some properties thereof leading to a better understanding of this new information-theoretic quantity.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland