Tracking brain dynamics via time-dependent network analysis.

Complex network analysis is currently employed in neuroscience research to describe the neuron pathways in the brain with a small number of computable measures that have neurobiological meaning. Connections in biological neural networks might fluctuate over time; therefore, surveillance can provide a more useful picture of brain dynamics than the standard approach that relies on a static graph to represent functional connectivity. Using the application of well-known measures of neural synchrony over short segments of brain activity in a time series, we attempted a time-dependent characterization of brain connectivity by investigating functional segregation and integration. In our implementation, a frequency-dependent time window was employed and regularly spaced (defined as overlapping segments), and a novel, parameter-free method was introduced to derive the required adjacency matrices. The resulting characterization was compared against conventional approaches that rely on static and time-evolving graphs, which are constructed from non-overlapping segments of arbitrarily defined durations. Our approach is demonstrated using EEG recordings during mental calculations. The derived consecutive values of network metrics were then compared with values from randomized networks. The results revealed the dynamic small-world character of the brain's functional connectivity, which otherwise can be hidden from estimators that rely on either long or stringent time-windows. Moreover, by involving a network-metric time series (NMTS) in a summarizing procedure that was based on replicator dynamics, consistent hubs that facilitated communication in the underlying networks were identified. Finally, the scale-free character of brain networks was also demonstrated based on the significant edges selected with the introduced approach.