  Entropic measures of complexity are able to quantify the information encoded
in complex network structures. Several entropic measures have been proposed in
this respect. Here we study the relation between the Shannon entropy and the
Von Neumann entropy of networks with a given expected degree sequence. We find
in different examples of network topologies that when the degree distribution
contains some heterogeneity, an intriguing correlation emerges between the two
entropies. This result seems to suggest that this kind of heterogeneity is
implying an equivalence between a quantum and a classical description of
networks, which respectively correspond to the Von Neumann and the Shannon
entropy.
