Revealing In-Block Nestedness: detection and benchmarking Albert Sol´e-Ribalta, Claudio J. Tessone, Manuel S. Mariani, Javier Borge-Holthoefer

[I’m posting this because it *sounds* fascinating, and applicable to pattern language, complex adaptive systems stuff, and the VSM. And also in the hope someone who understands the mathematics will explain it to me :-)]

Revealing In-Block Nestedness: detection and benchmarking
Albert Sol´e-Ribalta, Claudio J. Tessone, Manuel S. Mariani, Javier Borge-Holthoefer

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 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

Source: [1801.05620] Revealing In-Block Nestedness: detection and benchmarking