Abstract
In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis.
Highlights
The investigation of topological aspects of chemical structures concerns a major part of the research in chemical graph theory and mathematical chemistry [1,2,3,4]
A major contribution of this paper addresses the problem of finding bounds for the entropies of hierarchical graphs, which often occurs in chemical graph theory and computational and systems biology
Summary and Conclusion In this paper, we investigated the problem of finding entropy bounds for hierarchical graphs
Summary
The investigation of topological aspects of chemical structures concerns a major part of the research in chemical graph theory and mathematical chemistry [1,2,3,4]. QSAR (Quantitative structure-activity relationship) deals with descripting pharmacokinetic processes as well as biological activity or chemical reactivity [10,11]. QSPR (Quantitative Structure-Property Relationship) generally addresses the problem to convert chemical structures into molecular descriptors which are relevant to a physico-chemical property or a biological activity [11,12]. A main problem in QSPR is to investigate relationships between molecular structure and physicochemical properties, e.g., the topological complexity of chemical structures [7,13,14,11]
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