In complex systems, individual components interact with each other often in non-linear ways via a non-trivial network of interactions.The structure of such network of interactions affects that system's dynamics and conveys information about the functional needs of thesystem, its evolution, and the role of individual units. For these reasons, network analysis has become a cornerstone of fields as diverse as systems biology, economics and sociology.In these fields, the advance of technology has boosted our capacity to gather increasing amounts of data on large complex systems. Unfortunately, our understanding has not grown proportionally. Two of the main reasons for such disparity are: (i) that we lack a complete set of tools to summarize information and transform it into practical knowledge; (ii) he reliability of network data is often a source of concern and poses serious questions about the validity of the conclusions of network studies.The proposed research addresses these the two issues outlined above based on two premises: (i) that group-based models, or more generally block models, are good descriptors of patterns of interactions between nodes in a network, and (ii) that every observed pattern of interactions is the result of the overlay of several block models.The overarching goal of the proposal is to develop a framework that enables the identification of a set of orthogonal block models, and the discovery of complex networks from sparse/incomplete empirical data sets; and to apply this framework to problems in systems biology.The research I propose is innovative in its ideas and will shed light on the mechanisms that shape network structure. Importantly, because the methodology I will develop is based solely on the topology and is independent of network context, the outcomes from this research are bound to have a major impact in a number of areas including social sciences, economics and biology.