FC Barcelona and the triadic closure property
FC Barcelona is a professional football (soccer) club based in Barcelona, Spain. The club is famous for using a quick, short passing style known as “Tiki- Taka.” And used this style to dominate Europe from 2008-2012. Tiki-taka takes advantage of the club’s formation which utilizes four defenders, three midfielders, and three forwards set up in a series of triangles. Barcelona’s tactics bring to mind one of the most basic laws of graph theory, the law of triadic closure.
Barcelona is famous for playing a very attack minded 4-3-3 (4 defenders, 3 midfielders, 3 forwards). As we can see in the picture above, the team is set up so that there are always multiple passing angles available to the player on the ball. We can make the formation diagram into a closed network, with the players acting as our nodes, and the primary and most obvious passing routes represented by edges.
We can see here that every node in the network satisfies the triadic closure property. Every single node is connected to another edge signifying at the minimum a weak relationship between the two nodes. In addition each node can form at least one triangle with two other nodes. These triangles are the strength of Barcelona’s tactics they enabled a safe passing option for every player on the pitch as well as provided creative angles of attack for the team to exploit. Because this is one team we can assume that everybody on the team knows each other and that the links between them are all strong, positive links. This creates a structurally stable network and team chemistry that can be seen when watching Barcelona play. Below is a video that shows examples of this fluid passing style in action. Take a look at it, even if you are not a soccer fan it is a great example of teamwork and understanding within a group of individuals.