  Exponential random graph theory is the complex network analog of the
canonical ensemble theory from statistical physics. While it has been
particularly successful in modeling networks with specified degree
distributions, a naive model of a clustered network using a graph Hamiltonian
linear in the number of triangles has been shown to undergo an abrupt
transition into an unrealistic phase of extreme clustering via triangle
condensation. Here we study a non-linear graph Hamiltonian that explicitly
forbids such a condensation and show numerically that it generates an
equilibrium phase with specified intermediate clustering.
