  We consider Gallai's graph Modular Decomposition theory for network
analytics. On the one hand, by arguing that this is a choice tool for
understanding structural and functional similarities among nodes in a network.
On the other, by proposing a model for random graphs based on this
decomposition. Our approach establishes a well defined context for hierarchical
modeling and provides a solid theoretical framework for probabilistic and
statistical methods. Theoretical and simulation results show the model
acknowledges scale free networks, high clustering coefficients and small
diameters all of which are observed features in many natural and social
networks.
