Recent developments in quantitative graph theory: information inequalities for networks.

PloS One
Matthias Dehmer, Lavanya Sivakumar

Abstract

In this article, we tackle a challenging problem in quantitative graph theory. We establish relations between graph entropy measures representing the structural information content of networks. In particular, we prove formal relations between quantitative network measures based on Shannon's entropy to study the relatedness of those measures. In order to establish such information inequalities for graphs, we focus on graph entropy measures based on information functionals. To prove such relations, we use known graph classes whose instances have been proven useful in various scientific areas. Our results extend the foregoing work on information inequalities for graphs.

References

Dec 1, 1966·Psychometrika·G Sabidussi
Mar 1, 1968·The Bulletin of Mathematical Biophysics·A Mowshowitz
Jul 12, 2003·SAR and QSAR in Environmental Research·D Bonchev
Sep 5, 2008·PloS One·Matthias DehmerFrank Emmert-Streib
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kartik Anand, Ginestra Bianconi
Jan 20, 2011·PloS One·Matthias DehmerFrank Emmert-Streib
Jun 7, 2011·IET Systems Biology·F Emmert-Streib, M Dehmer

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Citations

Jun 21, 2012·PloS One·Lavanya Sivakumar, Matthias Dehmer
Dec 19, 2020·Entropy·Yamila M Omar, Peter Plapper

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