Inferences on the Watts-Strogatz Model: A Study on Brain Functional Connectivity

Modelling real-world networks allows investigating the structure and the dynamics of such networks, which led to significant developments in various scientific fields. One of the most used models in these investigations is the Watts-Strogatz, with a structure composed of high clustering and short path lengths known as small-world networks. This model proposes an interesting gradient between regular and random networks, but its generating process, which relies on a single rewiring probability parameter, is hard to access and to manipulate. In order to study the mechanics of the Watts-Strogatz model, the present work proposes a new method based on deep neural networks that could estimate its probability p. To illustrate its applicability, neuroimaging and phenotypic resting-state fMRI data were used from patients with ADHD and typical development children, obtained from the ADHD-200 database. The neural network efficiently estimated the probability parameter, resulting in small-world graphs for functional brain connectivity with a mean ± s.e.m. p distribution of 0.804 ± 0.003. Despite no difference was found considering the gender or diagnosis of participants, the generalized linear model revealed age as a significant predictor of p (mean ± s.e.m.: 4.410 ± 0.877; p < 0.001), indicating a great effect of neurodevelopment on the brain network's structure. The proposed approach is promising in estimating the probability of the Watts-Strogatz model, and its application has the potential to improve investigations of network connectivity with a relatively efficient and simple framework.