PLoS ONE (Aug 2008)

Entropy bounds for hierarchical molecular networks.

  • Matthias Dehmer,
  • Stephan Borgert,
  • Frank Emmert-Streib

DOI
https://doi.org/10.1371/journal.pone.0003079
Journal volume & issue
Vol. 3, no. 8
p. e3079

Abstract

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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.