Community detection in weighted brain connectivity networks beyond the resolution limit

Graph theory provides a powerful framework to investigate brain functional connectivity networks and their modular organization. However, most graph-based methods suffer from a fundamental resolution limit that may have affected previous studies and prevented detection of modules, or "communities", that are smaller than a specific scale. Surprise, a resolution-limit-free function rooted in discrete probability theory, has been recently introduced and applied to brain networks, revealing a wide size-distribution of functional modules (Nicolini and Bifone, 2016), in contrast with many previous reports. However, the use of Surprise is limited to binary networks, while brain networks are intrinsically weighted, reflecting a continuous distribution of connectivity strengths between different brain regions. Here, we propose Asymptotical Surprise, a continuous version of Surprise, for the study of weighted brain connectivity networks, and validate this approach in synthetic networks endowed with a ground-truth modular structure. We compare Asymptotical Surprise with leading community detection methods currently in use and show its superior sensitivity in the detection of small modules even in the presence of noise and intersubject variability such as those observed in fMRI data. We apply our novel approach to functional connectivity networks from resting state fMRI experiments, and demonstrate a heterogeneous modular organization, with a wide distribution of clusters spanning multiple scales. Finally, we discuss the implications of these findings for the identification of connector hubs, the brain regions responsible for the integration of the different network elements, showing that the improved resolution afforded by Asymptotical Surprise leads to a different classification compared to current methods.