Temporal Hyperbolic Graphs as Null Models for Brain Dynamics

Null models are crucial for determining the degree of significance when testing hypotheses about brain dynamics modeled as a temporal complex network [7, 12]. The comparison between the hypothesis being tested on empirical data and on the null model enables us to assess the extent to which an apparently remarkable feature of the former can be attributed to randomness. In this work, we consider networks generated from resting-state functional magnetic resonance imaging (fMRI) signals from the Human Connectome Project [1] using standard processing techniques [9]. The network nodes correspond to brain regions while the edges represent the presence of a correlation greater than a certain value betweenthe signals of two regions. Over time, edges may appear and disappear, indicating that the associated correlation may jump above and below a certain value. While null models for static networks have been studied extensively [12, 4, 2, 6], there is a lack of attention to temporal networks. Therefore, our investigation focuses on the study of temporal null models. In doing so, we focus on the ability of the null models to reproduce the temporal small-worldness present in the empirical data, a property associated with the efficient exchange of information at local and global scales over time.