Note on von Neumann and Rényi Entropies of a Graph

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2017_Hogben_NoteVonNeuman.pdf (412.03 KB)

Date

2017-05-15

Authors

Dairyko, Michael
Hogben, Leslie
Lin, Jephian
Hogben, Leslie
Lockhart, Joshua
Roberson, David
Severini, Simone
Young, Michael

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Authors

Hogben, Leslie

Person

Organizational Units

Electrical and Computer Engineering

Organizational Unit

Mathematics

Organizational Unit

Department

Electrical and Computer EngineeringMathematics

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.

Comments

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.