Entropy of weighted graphs with Randić weights

Zengqiang Chen; Matthias Dehmer; Frank Emmert-Streib; Yongtang Shi

doi:10.3390/e17063710

Entropy of weighted graphs with Randić weights

Zengqiang Chen
, Matthias Dehmer^*
, Frank Emmert-Streib
, Yongtang Shi

^*Corresponding author for this work

Nankai University
Universität der Bundeswehr München
Private University for Health Sciences, Medical Informatics and Technology
Tampere University

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

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 Randić weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.

Original language	English
Pages (from-to)	3710-3723
Number of pages	14
Journal	Entropy
Volume	17
Issue number	6
DOIs	https://doi.org/10.3390/e17063710
Publication status	Published - 5 Jun 2015
Externally published	Yes

Keywords

Extremal value
Graph entropy
Randić weight
Shannon's entropy
Weighted graphs

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10.3390/e17063710

Cite this

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title = "Entropy of weighted graphs with Randi{\'c} weights",

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 Bollob{\'a}s and Erd{\"o}s, 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.",

keywords = "Extremal value, Graph entropy, Randi{\'c} weight, Shannon's entropy, Weighted graphs",

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TY - JOUR

T1 - Entropy of weighted graphs with Randić weights

AU - Chen, Zengqiang

AU - Dehmer, Matthias

AU - Emmert-Streib, Frank

AU - Shi, Yongtang

PY - 2015/6/5

Y1 - 2015/6/5

N2 - 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 Randić weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.

AB - 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 Randić weight. As a result, we derived statements on dendrimers that have been proven useful for applications. Finally, some open problems are presented.

KW - Extremal value

KW - Graph entropy

KW - Randić weight

KW - Shannon's entropy

KW - Weighted graphs

UR - https://www.scopus.com/pages/publications/84934300047

U2 - 10.3390/e17063710

DO - 10.3390/e17063710

M3 - Article

AN - SCOPUS:84934300047

SN - 1099-4300

VL - 17

SP - 3710

EP - 3723

JO - Entropy

JF - Entropy

IS - 6

ER -

Entropy of weighted graphs with Randić weights

Abstract

Keywords

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