In this talk, we establish a connection between network models (statistical models for random graphs), graphical models, and exchangeable and summarized random matrices. This relationship can be used in order to better understand the behavior of random graphs, and come up with statistical models that are both "marginalizable" and "extendable". In particular, this enables us to show that the degree distribution of an observed network is sufficient for statistical models that are both exchangeable and summarized. The connection to de Finetti theorem is also discussed.