Notes on the values of the volume entropy

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.