  Based on Jaynes' maximum entropy principle, exponential random graphs provide
a family of principled models that allow the prediction of network properties
as constrained by empirical data (observables). However, their use is often
hindered by the degeneracy problem characterized by spontaneous
symmetry-breaking, where predictions fail. Here we show that degeneracy appears
when the corresponding density of states function is not log-concave, which is
typically the consequence of nonlinear relationships between the constraining
observables. Exploiting these nonlinear relationships here we propose a
solution to the degeneracy problem for a large class of systems via
transformations that render the density of states function log-concave. The
effectiveness of the method is illustrated on examples.
