Note on von Neumann and Rényi Entropies of a Graph

Date
2017-05-15
Authors
Dairyko, Michael
Hogben, Leslie
Lin, Jephian
Lockhart, Joshua
Roberson, David
Severini, Simone
Young, Michael
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Abstract

We conjecture that all connected graphs of order n have von Neumann entropy at least as great as the star K1;n1 and prove this for almost all graphs of order n. We show that connected graphs of order n have Renyi 2-entropy at least as great as K1;n1 and for > 1, Kn maximizes Renyi -entropy over graphs of order n. We show that adding an edge to a graph can lower its von Neumann entropy.

Description

This is a manuscript of an article published as Dairyko, Michael, Leslie Hogben, Jephian C-H. Lin, Joshua Lockhart, David Roberson, Simone Severini, and Michael Young. "Note on von Neumann and Rényi entropies of a graph." Linear Algebra and its Applications 521 (2017): 240-253. DOI: 10.1016/j.laa.2017.01.037. Posted with permission.

Keywords
entropy, quantum, Laplacian, graph, matrix
Citation
DOI
Collections