Linear and Optimization Hamiltonians in Clustered Exponential Random Graph Modeling

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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.