PERCeIDs: PERiodic CommunIty Detection Many complex networked systems, both natural and humanmade, exhibit periodic behavior driven by underlying seasonal processes: election cycles and regular sporting events in social networks, cell cycle phases in gene networks, and load variation in infrastructure networks due to weather or daylight patterns. The natural periodicity may vary across network communities. At the same time this periodic community behavior is central to (i) understating the overall system dynamics and (ii) for detection of the communities themselves. The predominant approach to dynamic community detection first detects communities and then as a second step quantify seasonality in their activity. How to jointly detect communities and their inherent periodicity, while also accounting for nonperiodic oneoff events? We propose PERCeIDs, a framework for periodic overlapping community detection from temporal interaction data. We model observed pairwise interaction activity as a mixture of periodic and outlier (nonperiodic) components. We explicitly enforce periodic structure within our model by learning a succinct Ramanujan basis dictionary for community behaviors. By explicitly modeling periodicity, PERCeIDs outperforms baselines on both detecting highly overlapping communities with up to 2fold improvement in NMI compared to stateoftheart baselines, while offering an interpretable temporal structure for discovered communities in the dataset. Implementation of our method can be found at http:www.cs.albany.edupetkolabcode.html.

Periodicity Detection of Node Behaviour in Opportunistic Mobile Social Networks The recent rise of networks that rely on human mobility, such as opportunistic mobile social networks (OMSNs), has prompted the need for methods that detect the periodic patterns of node movements. Knowledge of the periodicity of node behaviour is essential to design effective and efficient network protocols in such networks. Node behaviour in OMSNs is typically characterized by the node contact patterns. In fact, node connections in these networks occur intermittently, resulting in sparse contact data. Consequently, the traditional periodicity detection methods, e.g. the FFT periodogram and autocorrelation, that favour complete, regularlysampled timeseries data are unsuitable in this setting. In this paper, we exploit the LombScargle periodogram, initially designed to handle incomplete or irregular sampling data, to identify node behaviour periodicity in OMSNs. Using simulation driven by real human contact traces, we show that the technique is able to accurately detect the behaviour periodicity of majority nodes in the network, even for those with a high level of sparsity contact data.