Using Network Science to Analyse Football Passing Networks: Dynamics, Space, Time, and the Multilayer Nature of the Game

Beware of the Small-World Neuroscientist!

Time irreversibility is a common signature of nonlinear processes and a fundamental property of non-equilibrium systems driven by non-conservative forces. A time series is said to be reversible if its statistical properties are invariant regardless of the direction of time. Here, we propose the Time Reversibility from Ordinal Patterns method (TiROP) to assess time-reversibility from an observed finite time series. TiROP captures the information of scalar observations in time forward as well as its time-reversed counterpart by means of ordinal patterns. The method compares both underlying information contents by quantifying its (dis)-similarity via the Jensen-Shannon divergence. The statistic is contrasted with a population of divergences coming from a set of surrogates to unveil the temporal nature and its involved time scales. We tested TiROP in different synthetic and real, linear, and non-linear time series, juxtaposed with results from the classical Ramsey’s time reversibility test. Our results depict a novel, fast-computation, and fully data-driven methodology to assess time-reversibility with no further assumptions over data. This approach adds new insights into the current non-linear analysis techniques and also could shed light on determining new physiological biomarkers of high reliability and computational efficiency.

We quantified the spatial and temporal entropy related to football teams and their players by means of a pass-based interaction. First, we calculated the spatial entropy associated to the positions of all passes made by a football team during a match, obtaining a spatial entropy ranking of Spanish teams during the 2017/2018 season. Second, we investigated how the player’s average location in the field is related to the amount of entropy of his passes. Next, we constructed the temporal passing networks of each team and computed the deviation of their network parameters along the match. For each network parameter, we obtained the permutation entropy and the statistical complexity of its temporal fluctuations. Finally, we investigated how the permutation entropy (and statistical complexity) of the network parameters was related to the total number of passes made by a football team. Our results show that (i) spatial entropy changes according to the position of players in the field, and (ii) the organization of passing networks change during a match and its evolution can be captured measuring the permutation entropy and statistical complexity of the network parameters, allowing to identify what parameters evolve more randomly.

We investigated how the organization of functional brain networks was related to cognitive reserve (CR) during a memory task in healthy aging. We obtained the magnetoencephalographic functional networks of 20 elders with a high or low CR level to analyse the differences at network features. We reported a negative correlation between synchronization of the whole network and CR, and observed differences both at the node and at the network level in: the average shortest path and the network outreach. Individuals with high CR required functional networks with lower links to successfully carry out the memory task. These results may indicate that those individuals with low CR level exhibited a dual pattern of compensation and network impairment, since their functioning was more energetically costly to perform the task as the high CR group. Additionally, we evaluated how the dynamical properties of the different brain regions were correlated to the network parameters obtaining that entropy was positively correlated with the strength and clustering coefficient, while complexity behaved conversely. Consequently, highly connected nodes of the functional networks showed a more stochastic and less complex signal. We consider that network approach may be a relevant tool to better understand brain functioning in aging.