On the possible values of the entropy of undirected graphs

TL;DR

This paper investigates the entropy of undirected graphs, proving finiteness of possible entropy values up to any integer and explicitly determining all values up to four.

Contribution

It establishes the finiteness of entropy values for undirected graphs up to any integer and characterizes all such values for entropy up to four.

Findings

Number of possible entropy values up to k is finite.

All entropy values up to four are explicitly determined.

Provides a foundation for understanding entropy in undirected graphs.

Abstract

The entropy of a digraph is a fundamental measure which relates network coding, information theory, and fixed points of finite dynamical systems. In this paper, we focus on the entropy of undirected graphs. We prove that for any integer $k$ the number of possible values of the entropy of an undirected graph up to $k$ is finite. We also determine all the possible values for the entropy of an undirected graph up to the value of four.