Information inequalities and Generalized Graph Entropies

TL;DR

This paper explores relationships between Shannon and Rényi entropies for network structures, establishing formal inequalities and connections between different graph entropy measures, with explicit results for specific graph classes.

Contribution

It introduces formal inequalities linking Shannon and Rényi entropies for graphs, and connects classical partition-based and functional-based graph entropies, including explicit inequalities for certain graph classes.

Findings

Established implicit inequalities between Shannon and Rényi entropies for graphs.

Derived inequalities connecting partition-based and functional-based graph entropies.

Provided explicit inequalities for special classes of graphs.

Abstract

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy have been considered for this study. Our main results involve establishing formal relationship, in the form of implicit inequalities, between these two kinds of measures when defined for graphs. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and the functional-based entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.