Journal
ENTROPY
Volume 17, Issue 6, Pages 3710-3723Publisher
MDPI
DOI: 10.3390/e17063710
Keywords
Shannon's entropy; graph entropy; weighted graphs; extremal value; Randi weight
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Funding
- Austrian Science Funds [P26142]
- German Federal Ministry of Education and Research (BMBF) (Project RiKoV) [13N12304]
- National Science Foundation of China [61174094]
- Natural Science Foundation of Tianjin [14JCYBJC18700]
- National Science Foundation of China (NSFC)
- Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT)
- China Postdoctoral Science Foundation
- Austrian Science Fund (FWF) [P26142] Funding Source: Austrian Science Fund (FWF)
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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.
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