Edge-centric functional connectivity (eFC) has recently been proposed to characterise the finest time resolution on the FC dynamics without the concomitant assumptions of sliding-window approaches. Here, we lay the mathematical foundations for the edge-centric analysis and examine its main findings from a quantitative perspective. The proposed framework provides a theoretical explanation for the observed occurrence of high-amplitude edge cofluctuations across datasets and clarifies why a few large events drive the node-centric FC (nFC). Our exposition also constitutes a critique of the edge-centric approach as currently applied to functional MRI (fMRI) time series. The central argument is that the existing findings based on edge time series can be derived from the static nFC under a null hypothesis that only accounts for the observed static spatial correlations and not the temporal ones. Challenging our analytic predictions against fMRI data from the Human Connectome Project confirms that the nFC is sufficient to replicate the eFC matrix, the edge communities, the large cofluctuations, and the corresponding brain activity mode. We conclude that the temporal structure of the edge time series has not so far been exploited sufficiently and encourage further work to explore features that cannot be explained by the presented static null model.
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