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Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. Temporal networks provide a framework to describe the time-resolve interactions between components of a system. An important task when investigating such systems is to extract a simplified view of the temporal network, which can be done via dynamic community detection or clustering. Several works have generalized existing community detection methods for static networks to temporal networks, but they usually rely on temporal aggregation over time windows, the assumption of an underlying stationary process, or sequences of different stationary epochs. Here, we derive a method based on a dynamical process evolving on the temporal network and restricted by its activation pattern that allows to consider the full temporal information of the system. Our method allows dynamics that do not necessarily reach a steady state, or follow a sequence of stationary states. Our framework encompasses several well-known heuristics as special cases. We show that our method provides a natural way to disentangle the different natural dynamical scales present in a system. We demonstrate our method abilities on synthetic and real-world examples.
Research into detection of dense communities has recently attracted increasing attention within network science, various metrics for detection of such communities have been proposed. The most popular metric -- Modularity -- is based on the so-called
Time-stamped data are increasingly available for many social, economic, and information systems that can be represented as networks growing with time. The World Wide Web, social contact networks, and citation networks of scientific papers and online
Embedding a network in hyperbolic space can reveal interesting features for the network structure, especially in terms of self-similar characteristics. The hidden metric space, which can be thought of as the underlying structure of the network, is ab
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure. The K-core
Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for unweighted commu