The authors develop a rigorous and interpretable statistical model for networks using their shell structure to construct minimal sufficient statistics. The model provides the formalism necessary for using k-cores in statistical considerations of random graphs, and in particular social networks. It cannot be specialized to any known degree-centric model and does not generalize Erdos-Renyi. They propose a sampling algorithm for constructing all graphs with a given shell structure, and an MCMC algorithm to simulate from the model. These algorithms will serve as a basis for parameter estimation and model fit tests.