Brain dynamics can be modeled as a temporal brain network starting from the activity of different brain regions in functional magnetic resonance imaging (fMRI) signals. When validating hypotheses about temporal networks, it is important to use an appropriate statistical null model that shares some features with the treated empirical data. The purpose of this work is to contribute to the theory of temporal null models for brain networks by introducing the random temporal hyperbolic (RTH) graph model, an extension of the random hyperbolic (RH) graph, known in the study of complex networks for its ability to reproduce crucial properties of real-world networks. We focus on temporal small-worldness which, in the static case, has been extensively studied in real-world complex networks and has been linked to the ability of brain networks to efficiently exchange information. We compare the RTH graph model with standard null models for temporal networks and show it is the null model that best reproduces the small-worldness of resting brain activity. This ability to reproduce fundamental features of real brain networks, while adding only a single parameter compared with classical models, suggests that the RTH graph model is a promising tool for validating hypotheses about temporal brain networks.

We show that the random temporal hyperbolic (RTH) graph is a suitable null model for testing hypotheses about brain dynamics, after comparing it with the current state of the art and two other geometric null models. The static version of this theoretical model captures properties of various real-world networks, and its temporal version exhibits the temporal small-world property, for which we propose a new proper temporal definition. In particular, we show that the model best reproduces the temporal small-worldness measured in the empirical temporal network extracted from fMRI signals.

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Competing Interests

Competing Interests: The authors have declared that no competing interests exist.

Author notes

Handling Editor: Mikail Rubinov

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