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

A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod's model for cultural dissemination.

As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors—sampling the most connected, random, and friends of random individuals—in three complex social networks—a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals—early and accurate detection of epidemic emergence and peak, and general situational awareness—we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R₀). For diseases with a low R₀, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R₀ is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information. As public health agencies strive to harness big data to improve outbreak surveillance, they face the challenge of extracting meaningful information that can be directly used to improve public health, without incurring additional costs. In this article, we address the question: Which nodes in a social network should be selectively monitored to detect and monitor outbreaks as early and accurately as possible? We derive best-case performance scenarios, and show that a practical strategy for data collection–recruiting friends of randomly selected individuals–is expected to perform reasonably well, in terms of the timing and reliability of the epidemiological information collected.

To help health policy makers gain response time to mitigate infectious disease threats, it is essential to have an efficient epidemic surveillance. One common method of disease surveillance is to carefully select nodes (sentinels, or sensors) in the network to report outbreaks. One would like to choose sentinels so that they discover the outbreak as early as possible. The optimal choice of sentinels depends on the network structure. Studies have addressed this problem for static networks, but this is a first step study to explore designing surveillance systems for early detection on temporal networks. This paper is based on the idea that vaccination strategies can serve as a method to identify sentinels. The vaccination problem is a related question that is much more well studied for temporal networks. To assess the ability to detect epidemic outbreaks early, we calculate the time difference (lead time) between the surveillance set and whole population in reaching 1% prevalence. We find that the optimal selection of sentinels depends on both the network’s temporal structures and the infection probability of the disease. We find that, for a mild infectious disease (low infection probability) on a temporal network in relation to potential disease spreading (the Prostitution network), the strategy of selecting latest contacts of random individuals provide the most amount of lead time. And for a more uniform, synthetic network with community structure the strategy of selecting frequent contacts of random individuals provide the most amount of lead time.

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.