Revealing In-Block Nestedness: detection and benchmarking

TL;DR

This paper introduces the concept of in-block nestedness to better understand complex network structures, providing new methods to detect and benchmark this property in real and synthetic networks, challenging existing theories.

Contribution

It presents the novel concept of in-block nestedness and develops optimization methods to detect it, addressing flaws in previous assessments of nested and modular structures.

Findings

In-block nestedness is prevalent in real networks.

New methods successfully identify in-block nestedness.

Findings challenge existing models of network topology.

Abstract

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.