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Entropy 2014, 16(10), 5416-5427;

A Note on Distance-based Graph Entropies

College of Computer and Control Engineering, Nankai University, No. 94 Weijin Road, 300071 Tianjin, China
Department of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Institute for Bioinformatics and Translational Research, UMIT, Eduard Wallnoefer Zentrum A-6060, Hall in Tyrol, Austria
Center for Combinatorics and LPMC-TJKLC, Nankai University, No. 94 Weijin Road, 300071 Tianjin, China
Author to whom correspondence should be addressed.
Received: 26 July 2014 / Revised: 18 September 2014 / Accepted: 15 October 2014 / Published: 20 October 2014
(This article belongs to the Special Issue Complex Systems and Nonlinear Dynamics)
Full-Text   |   PDF [161 KB, uploaded 24 February 2015]


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. View Full-Text
Keywords: entropy; Shannon’s entropy; graph entropy; distance; networks entropy; Shannon’s entropy; graph entropy; distance; networks
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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Chen, Z.; Dehmer, M.; Shi, Y. A Note on Distance-based Graph Entropies. Entropy 2014, 16, 5416-5427.

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