Absence of a resolution limit in in-block nestedness
Nestedness refers to a hierarchical organization of complex networks where a given node’s neighbors tend to form a subset of the neighborhoods of higher-degree nodes. Although nestedness has been traditionally interpreted as a macroscopic property that involves all the nodes of the network, recent works have reinterpreted it as a mesoscopic network property, by revealing that interactions in diverse empirical networks are often arranged into blocks that exhibit an internally nested structure. Inspired by the popular modularity function, these works rely on a quality function – called in-block nestedness – that assumes a partition of the nodes into blocks that exhibit an internal nested structure. A potential limitation of this approach is that the optimization of modularity (and related quality functions) notoriously suffers from resolution limits that impair the detectability of small blocks. Yet, we do not know whether the in-block nestedness function may exhibit similar resolution limits. Here, we provide numerical and analytical evidence that the in-block nestedness function lacks a resolution limit, which implies that our capacity to detect correct partitions in networks via its maximization depends solely on the accuracy of the optimization algorithms.