Linear and optimization Hamiltonians in clustered exponential random graph modeling

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 nave 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 nonlinear graph Hamiltonian that explicitly forbids such a condensation and show numerically that it generates an equilibrium phase with specified intermediate clustering.