A Note on Distance-based Graph Entropies
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-10-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/10/5416 |
| _version_ | 1828113851633106944 |
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| author | Zengqiang Chen Matthias Dehmer Yongtang Shi |
| author_facet | Zengqiang Chen Matthias Dehmer Yongtang Shi |
| author_sort | Zengqiang Chen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T12:15:24Z |
| format | Article |
| id | doaj.art-d384fc37f1544d0b9ed51bca60c5b9bb |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:15:24Z |
| publishDate | 2014-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d384fc37f1544d0b9ed51bca60c5b9bb2022-12-22T04:24:20ZengMDPI AGEntropy1099-43002014-10-0116105416542710.3390/e16105416e16105416A Note on Distance-based Graph EntropiesZengqiang Chen0Matthias Dehmer1Yongtang Shi2College of Computer and Control Engineering, Nankai University, No. 94 Weijin Road, 300071 Tianjin, ChinaDepartment of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, GermanyCenter for Combinatorics and LPMC-TJKLC, Nankai University, No. 94 Weijin Road, 300071 Tianjin, ChinaA 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.http://www.mdpi.com/1099-4300/16/10/5416entropyShannon’s entropygraph entropydistancenetworks |
| spellingShingle | Zengqiang Chen Matthias Dehmer Yongtang Shi A Note on Distance-based Graph Entropies Entropy entropy Shannon’s entropy graph entropy distance networks |
| title | A Note on Distance-based Graph Entropies |
| title_full | A Note on Distance-based Graph Entropies |
| title_fullStr | A Note on Distance-based Graph Entropies |
| title_full_unstemmed | A Note on Distance-based Graph Entropies |
| title_short | A Note on Distance-based Graph Entropies |
| title_sort | note on distance based graph entropies |
| topic | entropy Shannon’s entropy graph entropy distance networks |
| url | http://www.mdpi.com/1099-4300/16/10/5416 |
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