Detecting periodic time scales in temporal networks

Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for instance periodic activity patterns or structural changes. The detection of these time scales can be challenging from the direct observation of simple dynamical network properties like the activity of nodes or the density of links. Here we propose two new methods, which rely on already established static representations of temporal networks, namely supra-adjacency matrices and temporal event graphs. We define dissimilarity metrics extracted from these representations and compute their Fourier Transform to effectively identify dominant periodic time scales characterising the original temporal network. We demonstrate our methods using synthetic and real-world data sets describing various kinds of temporal networks. We find that while in all cases the two methods outperform the reference measures, the supra-adjacency based method identifies more easily periodic changes in network density, while the temporal event graph based method is better suited to detect periodic changes in the group structure of the network. Our methodology may provide insights into different phenomena occurring at multiple time-scales in systems represented by temporal networks.