  As new instances of nested organization --beyond ecological networks-- are
discovered, scholars are debating around the co-existence of two apparently
incompatible macroscale architectures: nestedness and modularity. The
discussion is far from being solved, mainly for two reasons. First, nestedness
and modularity appear to emerge from two contradictory dynamics, cooperation
and competition. Second, existing methods to assess the presence of nestedness
and modularity are flawed when it comes to the evaluation of concurrently
nested and modular structures. In this work, we tackle the latter problem,
presenting the concept of \textit{in-block nestedness}, a structural property
determining to what extent a network is composed of blocks whose internal
connectivity exhibits nestedness. We then put forward a set of optimization
methods that allow us to identify such organization successfully, both in
synthetic and in a large number of real networks. These findings challenge our
understanding of the topology of ecological and social systems, calling for new
models to explain how such patterns emerge.
