Linear and Optimization Hamiltonians in Clustered Exponential Random\n Graph Modeling

Exponential random graph theory is the complex network analog of the\ncanonical ensemble theory from statistical physics. While it has been\nparticularly successful in modeling networks with specified degree\ndistributions, a naive model of a clustered network using a graph Hamiltonian\nlinear in the number of triangles has been shown to undergo an abrupt\ntransition into an unrealistic phase of extreme clustering via triangle\ncondensation. Here we study a non-linear graph Hamiltonian that explicitly\nforbids such a condensation and show numerically that it generates an\nequilibrium phase with specified intermediate clustering.\n