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
naïve 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. We
also discuss some applications based on Hamiltonian-based
graph theory. |