To illustrate the problem of ad-hoc measures I constructed a network whose node degrees follows the so-called Champernowne artificially-constructed Borel normal constant thus indicating maximal entropy (and maximal entropy rate) by construction, though its edge density asymptotically approximates zero and thus the entropy rate of its adjacency matrix also converges to zero, in contradiction to the entropy rate of its degree sequence. So we presented a graph that, depending on the choice of description, has the same maximal and minimal information-content according to Shannon entropy for the same uninformative choice of distribution (uniform) in both cases, thereby establishing the fragility and description-dependent nature of Shannon entropy. Main collaborators: Narsis A. Kiani, Jesper Tegnér. See paper: J35.
