Solution for the properties of a clustered network.

We study Strauss's model of a network with clustering and present an analytic mean-field solution which is exact in the limit of large network size. Previous computer simulations have revealed a degenerate region in the model's parameter space in which triangles of adjacent edges clump together to form unrealistically dense subgraphs, and perturbation calculations have been found to break down in this region at all orders. Our solution shows that this region corresponds to a classic symmetry-broken phase and that the onset of the degeneracy corresponds to a first-order phase transition in the density of the network.