The analysis of temporal networks heavily depends on the analysis of time-respecting paths. However, before being able to model and analyze the time-respecting paths, we have to infer the timescales at which the temporal edges influence each other. In this work we introduce temporal path entropy, an information theoretic measure of temporal networks, with the aim to detect the timescales at which the causal influences occur in temporal networks. The measure can be used on temporal networks as a whole, or separately for each node. We find that the temporal path entropy has a non-trivial dependency on the causal timescales of synthetic and empirical temporal networks. Furthermore, we notice in both synthetic and empirical data that the temporal path entropy tends to decrease at timescales that correspond to the causal interactions. Our results imply that timescales relevant for the dynamics of complex systems can be detected in the temporal networks themselves, by measuring temporal path entropy. This is crucial for the analysis of temporal networks where inherent timescales are unavailable and hard to measure.

翻译：时间网络的分析高度依赖于时间尊重路径的分析。然而，在能够建模和分析时间尊重路径之前，我们必须推断时间边相互影响的时间尺度。本研究引入时间路径熵，一种信息论视角下的时间网络度量，旨在检测时间网络中因果影响发生的时间尺度。该度量可整体应用于时间网络，也可分别应用于每个节点。我们发现，时间路径熵对合成及实证时间网络的因果时间尺度存在非平凡依赖关系。此外，在合成数据和实证数据中均观察到，时间路径熵在对应于因果交互的时间尺度上趋于下降。我们的结果表明，通过测量时间路径熵，可在时间网络本身中检测到与复杂系统动态相关的时间尺度。这对于内在时间尺度未知且难以测量的时间网络分析至关重要。