Trajectories through temporal networks

Abstract What do football passes and financial transactions have in common? Both are networked walk processes that we can observe, where records take the form of timestamped events that move something tangible from one node to another. Here we propose an approach to analyze this type of data that extracts the actual trajectories taken by the tangible items involved. The main advantage of analyzing the resulting trajectories compared to using, e.g., existing temporal network analysis techniques, is that sequential, temporal, and domain-specific aspects of the process are respected and retained. As a result, the approach lets us produce contextually-relevant insights. Demonstrating the usefulness of this technique, we consider passing play within association football matches (an unweighted process) and e-money transacted within a mobile money system (a weighted process). Proponents and providers of mobile money care to know how these systems are used—using trajectory extraction we find that 73% of e-money was used for stand-alone tasks and only 21.7% of account holders built up substantial savings at some point during a 6-month period. Coaches of football teams and sports analysts are interested in strategies of play that are advantageous. Trajectory extraction allows us to replicate classic results from sports science on data from the 2018 FIFA World Cup. Moreover, we are able to distinguish teams that consistently exhibited complex, multi-player dynamics of play during the 2017–2018 club season using ball passing trajectories, coincidentally identifying the winners of the five most competitive first-tier domestic leagues in Europe.