Entropy of Weighted Graphs with Randić Weights

Entropy

Zengqiang Chen²  Matthias Dehmer³  Frank Emmert-Streib⁴  Yongtang Shi¹ 

[1] Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, China;College of Computer and Control Engineering, Nankai University, Tianjin 300071, China; E-Mail:;Department of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany;Computational Medicine and Statistical Learning Laboratory, Department of Signal Processing, Tampere University of Technology, FI-33720 Tampere, Finland; E-Mail:

关键词: Shannon’s entropy;    graph entropy;    weighted graphs;    extremal value;    Randić weight;   

DOI  :  10.3390/e17063710

来源: mdpi

【 摘 要 】

Shannon entropies for networks have been widely introduced. However, entropies for weighted graphs have been little investigated. Inspired by the work due to Eagle et al., we introduce the concept of graph entropy for special weighted graphs. Furthermore, we prove extremal properties by using elementary methods of classes of weighted graphs, and in particular, the one due to Bollobás and Erdös, which is also called the Randić weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.

【 授权许可】

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