  We consider a new model for complex networks whose underlying mechanism is
extending dense subgraphs. In the frustum model, we iteratively extend cliques
over discrete-time steps. For many choices of the underlying parameters, graphs
generated by the model densify over time. In the special case of the cone
model, generated graphs provably satisfy properties observed in real-world
complex networks such as the small world property and bad spectral expansion.
We finish with a set of open problems and next steps for the frustum model.
