
The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this talk we show how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs  entropies of network ensembles. The quantities we introduce here are shown to have relevance for formulation of null models of networks  and are shown to  contribute significantly in solving  inference problems emerging in the field of complex networks.
