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. Author manuscript; available in PMC: 2019 Sep 25.
Published in final edited form as: Nat Phys. 2019 Mar 25;15(4):313–320. doi: 10.1038/s41567-019-0459-y

Figure 2. Non-Markovian higher-order models can better capture the topology of paths in complex systems.

Figure 2

A rich source of path information is time-series data that capture interaction sequences between the components of a system (a). Focusing on pairwise interactions, network models abstract a system’s topology with nodes and links (b) while assuming that paths are transitive and Markovian (c). Due to the chronological ordering of interactions, the actual paths of indirect influence in time- series data (d) can deviate from this assumption. Focusing on paths rather than pairwise interactions, higher-order network models with, for example, state nodes (e) can capture the actual topology of indirect influence (f).