While current technology permits inference of dynamic brain networks over long time periods at high temporal resolution, the detailed structure of dynamic network communities during human seizures remains poorly understood. We introduce a new methodology that addresses critical aspects unique to the analysis of dynamic functional networks inferred from noisy data. We propose a dynamic plex percolation method (DPPM) that is robust to edge noise, and yields well-defined spatiotemporal communities that span forward and backwards in time. We show in simulation that DPPM outperforms existing methods in accurately capturing certain stereotypical dynamic community behaviors in noisy situations. We then illustrate the ability of this method to track dynamic community organization during human seizures, using invasive brain voltage recordings at seizure onset. We conjecture that application of this method will yield new targets for surgical treatment of epilepsy, and more generally could provide new insights in other network neuroscience applications.

We consider the problem of distinguishing classical (Erdős-Rényi) percolation from explosive (Achlioptas) percolation, under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations. This graph-valued stochastic process is composed of a latent and an observed non-stationary process, where the observed graph process is corrupted by Type I and Type II errors. This produces a hidden Markov graph model. We show that for certain choices of parameters controlling the noise, the classical (ER) percolation is visually indistinguishable from the explosive (Achlioptas) percolation model. In this setting, we compare two different criteria for discriminating between these two percolation models, based on a quantile difference (QD) of the first component’s size and on the maximal size of the second largest component. We show through data simulations that this second criterion outperforms the QD of the first component’s size, in terms of discriminatory power. The maximal size of the second component therefore provides a useful statistic for distinguishing between the ER and Achlioptas models of percolation, under physically motivated conditions for the birth and death of edges, and under noise. The potential application of the proposed criteria for percolation detection in clinical neuroscience is also discussed.