Entropy of Weighted Graphs with Randic Weights

被引：31
作者：
Chen, Zengqiang [1 ]
Dehmer, Matthias [2 ,3 ]
Emmert-Streib, Frank [4 ,5 ]
Shi, Yongtang [6 ,7 ]
机构：
[1] Nankai Univ, Coll Comp & Control Engn, Tianjin 300071, Peoples R China
[2] Univ Bundeswehr Munchen, Dept Comp Sci, D-85577 Neubiberg, Germany
[3] UMIT, Dept Mechatron & Biomed Comp Sci, A-6060 Hall In Tirol, Austria
[4] Tampere Univ Technol, Dept Signal Proc, Computat Med & Stat Learning Lab, FI-33720 Tampere, Finland
[5] Inst Biosci & Med Technol, Tampere 33520, Finland
[6] Nankai Univ, Ctr Combinator, Tianjin 300071, Peoples R China
[7] Nankai Univ, LPMC TJKLC, Tianjin 300071, Peoples R China
来源：
ENTROPY | 2015年 / 17卷 / 06期
基金：
中国博士后科学基金; 美国国家科学基金会; 奥地利科学基金会;
关键词：
Shannon's entropy; graph entropy; weighted graphs; extremal value; Randi weight; SUM-CONNECTIVITY INDEX; HYPER-WIENER INDEX; ZAGREB INDEXES; MOLECULAR GRAPHS; TREES; COMPLEXITY; NUMBER; ORDER; VERSION; EXTREMALITY;
D O I：
10.3390/e17063710
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
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 Bollobas and Erdos, which is also called the Randi weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.
引用
收藏
页码：3710 / 3723
页数：14
相关论文
共 66 条
[1]  
Abdo H, 2014, MATCH-COMMUN MATH CO, V72, P741
[2]  
Ahmadi MB, 2014, MATCH-COMMUN MATH CO, V72, P685
[3]  
Al-Fozan T, 2014, MATCH-COMMUN MATH CO, V72, P339
[4]   Measuring graph abstractions of software: An information-theory approach [J].
Allen, EB .
EIGHTH IEEE SYMPOSIUM ON SOFTWARE METRICS, PROCEEDINGS, 2002, :182-193
[5]  
[Anonymous], 1949, The mathematical theory of communication
[6]  
Arezoomand M, 2013, MATCH-COMMUN MATH CO, V69, P131
[7]  
Azari M, 2013, MATCH-COMMUN MATH CO, V70, P921
[8]  
Bollobás B, 1998, ARS COMBINATORIA, V50, P225
[9]   Degree Powers in Graphs: The Erdos-Stone Theorem [J].
Bollobas, Bela ;
Nikiforov, Vladimir .
COMBINATORICS PROBABILITY & COMPUTING, 2012, 21 (1-2) :89-105
[10]   Degree-based entropies of networks revisited [J].
Cao, Shujuan ;
Dehmer, Matthias .
APPLIED MATHEMATICS AND COMPUTATION, 2015, 261 :141-147
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