Football is also maths: Graph theory at the World Cup

On weekend, we had the opportunity to enjoy a maths chat-conference by Dr. Sáenz de Cabezón.

Eduardo Sáenz de Cabezón (read below for more information) demonstrated at the University of Murcia (Faculty of Mathematics but audotprium of Veterinary) that football is far more scientific than it first appears, using graph theory to dissect the legendary World Cup final between Spain and the Netherlands.

Nodes and Passes: The screen shows how each player becomes a node and each pass a line with a direction. The thickness and density of Spain's blue lines perfectly reflect that hyperconnected network that stifled the opposing team's play through sheer possession.

A Snapshot of Two Styles: The visual contrast in the slide is striking. In contrast to the dense and organized web of the Spanish team, the orange graph of the Netherlands shows much more dispersed, chaotic connections, dependent on individual players.

Science on the Bench: Analyzing the properties of the nodes allows us to measure a player's real impact, who distributes the ball best, and where the flow of play breaks down. Pure Big Data applied to tactics.

A brilliant way to demonstrate that maths is not boring, but the ultimate tool for understanding the patterns of the world (and of football). 

Common Problems & Applications of Graph Theory (read below to know a concepts summary)*

- Shortest Path Problem: Finding the most efficient route between two points. This forms the backbone of GPS navigation systems and routing protocols in networks.

- The Königsberg Problem: Investigating whether it is possible to traverse every bridge (edge) exactly once and return to the starting point (establishing the concept of an "Eulerian path").

- Social Network Analysis: Modeling friendships or interactions to analyze "degrees of separation" and influential nodes.

- Network Flow & Logistics: Maximizing the flow of materials, traffic, or data through a constrained system (such as optimizing delivery routes or preventing network bottlenecks).

- Colorability: Determining the minimum number of colors needed to color a map so no two adjacent regions share the same color (famously solved as the Four Color Theorem)

Eduardo Sáenz de Cabezón is a Spanish mathematician and professor of Computer Languages ​​and Systems at the University of La Rioja since 2001. He is known for his role as a science communicator, on the Spanish television program Órbita Laika (La 2 RTVE) and for being the creator of the YouTube channel Derivando, (in Spanish)

*Core Concepts of Graph theory.

- Vertices (Nodes): The fundamental units or objects being studied (e.g., people in a social network or cities on a map).

- Edges (Links): The connections, relationships, or pathways between vertices.

- Directed vs. Undirected: Edges can be bidirectional (undirected) or point in a specific direction (directed, like one-way streets or web hyperlinks).

- Weighted Graphs: Edges can carry "weights" or values, representing metrics like distance, cost, or time

Unknowledge: Facultad de Matemáticas de la UMU, Asfamures, Estalmat Murcia.