A Novel Framework Combining Social Network Analysis and Markov-Spectral Modelling for Assessing Team Coordination in Football: An Exploratory Case Study

Professional football is increasingly understood as a complex adaptive system where collective performance emerges from the interplay between structural organisation and dynamic ball circulation. While social network analysis (SNA) effectively captures static interaction patterns, it does not fully account for the probabilistic nature of possession flow. This exploratory study introduces an integrated framework combiningSNA with Markov-spectral modelling to provide a multi-layered characterisation of team coordination. Methods: The study employed a proof-of-concept design, analysing a high-performance team across two competitive matches. Passing event data were obtained through a commercial platform. The analytical framework integrated SNA metrics, computed using specialised software, with a Markov-spectral model implemented in a programming environment. This combination enabled quantification of structural properties alongside stochastic flow indices, including passing uncertainty, diffusion speed, network navigability and structural robustness. Results: The SNA layer identified a stable core of structurally influential players serving as primary hubs for ball circulation, alongside macro-level indicators of collective cohesion. The Markov-spectral layer revealed complementary information regarding the stochastic properties of possession flow, capturing aspects such as decision-making unpredictability, circulation efficiency and network resilience. Together, these findings illustrate how the integrated framework can characterise both structural stability and functional dynamics within team passing networks. Conclusion: The integration of SNA with Markov-spectral modelling offers a comprehensive toolkit for profiling team coordination in elite football, moving beyond static structural descriptions to quantify dynamic flow properties. This approach provides practitioners with complementary insights into both the organisation and functionality of team passing networks, supporting evidence-based tactical analysis and performance evaluation

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