Bovet Alexandre, Delvenne Jean-Charles, Lambiotte Renaud
Mathematical Institute, University of Oxford, Oxford, UK.
ICTEAM, Université catholique de Louvain, Louvain-la-Neuve, Belgium.
Sci Adv. 2022 May 13;8(19):eabj3063. doi: 10.1126/sciadv.abj3063. Epub 2022 May 11.
Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in these systems is to extract a simplified view of their time-dependent network of interactions. Community detection in temporal networks usually relies on aggregation over time windows or consider sequences of different stationary epochs. For dynamics-based methods, attempts to generalize static-network methodologies also face the fundamental difficulty that a stationary state of the dynamics does not always exist. Here, we derive a method based on a dynamical process evolving on the temporal network. Our method allows dynamics that do not reach a steady state and uncovers two sets of communities for a given time interval that accounts for the ordering of edges in forward and backward time. We show that our method provides a natural way to disentangle the different dynamical scales present in a system with synthetic and real-world examples.
由于同时存在不同的进程，许多系统呈现出复杂的时间动态。这些系统中的一项重要任务是提取其随时间变化的交互网络的简化视图。时间网络中的社区检测通常依赖于对时间窗口的聚合，或者考虑不同平稳时期的序列。对于基于动态的方法，试图推广静态网络方法也面临着一个基本困难，即动态的平稳状态并不总是存在。在这里，我们推导了一种基于在时间网络上演变的动态过程的方法。我们的方法允许动态过程不达到稳态，并为给定的时间间隔揭示两组社区，这两组社区考虑了正向和反向时间中边的顺序。我们通过合成和实际例子表明，我们的方法提供了一种自然的方式来解开系统中存在的不同动态尺度。
