This chapter concerns a model where the two constraint parameters are the densities of edges and of 2stars. We show that for any specified pair of values of the densities, an entropy maximizing graphon must be multipodal, with a uniform bound on the number of defining parameters. We then study two regions of the phase space, one near the bottom boundary and one near the center of the top boundary. Near the bottom boundary, we prove that there is a single bipodal phase, with parameters that are analytic functions of the edge and 2star densities. When the edge density e is close to ½ and the 2star density t is close to its maximum, the system exhibits a phase transition at e = ½; optimal graphons with e > ½ are "cliquelike", optimal graphons with e < ½ are "anticliquelike", and at e = ½ there are two inequivalent entropy maximizers. This suggests that the phase space for the edge-2star model consists of a single phase with a critical point, much as the phase space for physical materials such as water have a fluid phase with a liquid–gas transition ending at a critical point.