Abstract: A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties such as a meaningful structural interpretation and uniqueness. As classical work, many distance-based graph entropies, e.g., the ones due to Bonchev et al. and related quantities have been proposed and studied. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices with distance k to a given vertex. In particular, we investigate some properties thereof leading to a better understanding of this new information-theoretic quantity.
The information functional introduced in REF and defined as the number of vertices with distance k to a given vertex establishes the distance-based graph entropy.
A Note on Distance-based Graph Entropies
Entropy
Entropy
Mathematics Computer Science