Maximal entropy coverings and the information dimension of a complex network

Computing the information dimension dI of a complex network G requires covering G by a minimal collection of “boxes” of size s to obtain a set of probabilities, computing the entropy H(s), and quantifying how H(s) scales with log⁡s. We show that to determine whether dI≤dB holds for G, where dB is the box counting dimension, it is not sufficient to determine a minimal covering for each s. We introduce the new notion of a maximal entropy minimal covering of G, and a corresponding new definition of dI. The use of maximal entropy minimal coverings in many cases enhances the ability to compute dI.