From Sharma-Mittal to von-Neumann Entropy of a Graph
Discrete Mathematics
2019-02-21 v1 Disordered Systems and Neural Networks
Information Theory
Combinatorics
math.IT
Abstract
In this article, we introduce the Sharma-Mittal entropy of a graph, which is a generalization of the existing idea of the von-Neumann entropy. The well-known R{\'e}nyi, Thallis, and von-Neumann entropies can be expressed as limiting cases of Sharma-Mittal entropy. We have explicitly calculated them for cycle, path, and complete graphs. Also, we have proposed a number of bounds for these entropies. In addition, we have also discussed the entropy of product graphs, such as Cartesian, Kronecker, Lexicographic, Strong, and Corona products. The change in entropy can also be utilized in the analysis of growing network models (Corona graphs), useful in generating complex networks.
Keywords
Cite
@article{arxiv.1902.07548,
title = {From Sharma-Mittal to von-Neumann Entropy of a Graph},
author = {Souma Mazumdar and Amrik Singh and Supriyo Dutta and Sandeep Kumar Yadav and Partha Guha},
journal= {arXiv preprint arXiv:1902.07548},
year = {2019}
}