Physical Sciences and Mathematics Commons^™

Demystification Of Graph And Information Entropy, Bryce Frederickson

Undergraduate Honors Capstone Projects

Shannon entropy is an information-theoretic measure of unpredictability in probabilistic models. Recently, it has been used to form a tool, called the von Neumann entropy, to study quantum mechanics and network flows by appealing to algebraic properties of graph matrices. But still, little is known about what the von Neumann entropy says about the combinatorial structure of the graphs themselves. This paper gives a new formulation of the von Neumann entropy that describes it as a rate at which random movement settles down in a graph. At the same time, this new perspective gives rise to a generalization of von …