Higher-Order Patterns Reveal Causal Temporal Scales in Time Series Network Data

Luka V. Petrović, Anatol Eugen Wegner, Ingo Scholtes

Keywords: temporal networks, time scale, higher-order networks

TL;DR: We detect time-scales of a temporal network by measuring entropy of higher-order correlations between temporal edges.

Abstract: 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 an information theoretic measure, the causal path entropy, 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 causal 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 entropy tends to decrease at timescales that correspond to the causal paths. Our results imply that timescales relevant for the dynamics of complex systems can be detected in the temporal networks themselves, by measuring higher-order correlations. This is crucial for the analysis of temporal networks where inherent timescales are unavailable and hard to measure.

Type Of Submission: Extended abstract (max 4 main pages).

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Type Of Submission: Extended abstract.