  Existing information-theoretic frameworks based on maximum entropy network
ensembles are not able to explain the emergence of heterogeneity in complex
networks. Here, we fill this gap of knowledge by developing a classical
framework for networks based on finding an optimal trade-off between the
information content of a compressed representation of the ensemble and the
information content of the actual network ensemble. In this way not only we
introduce a novel classical network ensemble satisfying a set of soft
constraints but we are also able to calculate the optimal distribution of the
constraints. We show that for the classical network ensemble in which the only
constraints are the expected degrees a power-law degree distribution is
optimal. Also, we study spatially embedded networks finding that the
interactions between nodes naturally lead to non-uniform spread of nodes in the
space, with pairs of nodes at a given distance not necessarily obeying a
power-law distribution. The pertinent features of real-world air transportation
networks are well described by the proposed framework.
