Modular decomposition of graphs and hierarchical modeling

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.