Diffusion in Temporal Networks: London Tube passenger flows

This video shows the diffusion of visitation probabilities of a random walk in a temporal network that has been constructed based on time-stamped data on passenger flows in the London Tube network.

The left panel shows a random walk based on the empirical temporal network. This temporal network exhibits non-Markovian characteristics as shown in [1]. The right panel shows a random walk based on a a shuffled version of the same network, in which all order correlations are destroyed. This corresponds to a Markovian temporal network in which all time-respecting path statistics correspond to what is expected based on the static, time-aggregated network.

This video is an illustrative supporting animation for the following paper:

[1] Ingo Scholtes, Nicolas Wider, René Pfitzner, Antonios Garas, Claudio Juan Tessone and Frank Schweitzer: Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks, Nature Communications, Vol. 5, Article 5024, September 24, 2014