  Randomized network ensembles are the null models of real networks and are
extensivelly used to compare a real system to a null hypothesis. In this paper
we study network ensembles with the same degree distribution, the same
degree-correlations or the same community structure of any given real network.
We characterize these randomized network ensembles by their entropy, i.e. the
normalized logarithm of the total number of networks which are part of these
ensembles.
  We estimate the entropy of randomized ensembles starting from a large set of
real directed and undirected networks. We propose entropy as an indicator to
assess the role of each structural feature in a given real network.We observe
that the ensembles with fixed scale-free degree distribution have smaller
entropy than the ensembles with homogeneous degree distribution indicating a
higher level of order in scale-free networks.
