Notes on the values of the volume entropy

TL;DR

This paper investigates how adding edges or vertices affects the volume entropy of metric graphs and proposes an algorithm for calculating persistent volume entropy based on these insights.

Contribution

It provides formulas for the change in volume entropy when edges or vertices are added to metric graphs and introduces an algorithm for persistent volume entropy calculation.

Findings

Derived formulas for entropy change with edge addition

Analyzed entropy variation with vertex and surrounding edges

Suggested an algorithm for persistent volume entropy

Abstract

Volume entropy is an important invariant of metric graphs as well as Riemannian manifolds. In this note, we calculate the change of volume entropy when an edge is added to a metric graph. Using the first result, we investigate the change of volume entropy when a vertex and edges around it are added. In the second part, we estimate the value of the volume entropy which can be used to suggest an algorithm of calculating the persistent volume entropy of graphs.