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Entropy 2015, 17(6), 3710-3723; doi:10.3390/e17063710

Entropy of Weighted Graphs with Randi´c Weights

1
College of Computer and Control Engineering, Nankai University, Tianjin 300071, China
2
Department of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
3
Department of Mechatronics and Biomedical Computer Science, UMIT, A-6060 Hall in Tyrol, Austria
4
Computational Medicine and Statistical Learning Laboratory, Department of Signal Processing, Tampere University of Technology, FI-33720 Tampere, Finland
5
Institute of Biosciences and Medical Technology, 33520 Tampere, Finland
6
Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, China
*
Authors to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 18 May 2015 / Revised: 29 May 2015 / Accepted: 1 June 2015 / Published: 5 June 2015
View Full-Text   |   Download PDF [326 KB, uploaded 5 June 2015]   |  

Abstract

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. View Full-Text
Keywords: Shannon’s entropy; graph entropy; weighted graphs; extremal value; Randi´c weight Shannon’s entropy; graph entropy; weighted graphs; extremal value; Randi´c weight
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chen, Z.; Dehmer, M.; Emmert-Streib, F.; Shi, Y. Entropy of Weighted Graphs with Randi´c Weights. Entropy 2015, 17, 3710-3723.

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