College of Computer and Control Engineering, Nankai University, Tianjin 300071, China
Matthias Dehmer
Department of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Frank Emmert-Streib
Computational Medicine and Statistical Learning Laboratory, Department of Signal Processing, Tampere University of Technology, FI-33720 Tampere, Finland
Yongtang Shi
Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, China
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 Randi´c weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.
