Temporal Multilayer Fuzzy Quantum Graphs for Football Outcome Prediction and Player-Influence Ranking

Authors

  • Nivedita Kuity * Department of Computer and Information Science, Raiganj University, Raiganj–733134, India.
  • Laxminarayan Sahoo Department of Computer and Information Science, Raiganj University, Raiganj–733134, India.

https://doi.org/10.48314/tsc.v1i3.69

Abstract

Identifying structurally influential football players and predicting match outcomes from player interactions are challenging because event networks are temporal and multi-relational. This study proposes a Temporal Multilayer Fuzzy QuantumGraph framework that combines fuzzyweighted passing, defensive, possession, and spatial-progression layers with a continuous-time quantum walk. A real-symmetric aggregate adjacency matrix is used as the Hamiltonian so that the evolution is unitary. The framework is illustrated using event data from all 64 matches of the 2018 FIFA World Cup in StatsBomb Open Data. Fifteen-minute temporal windows are aggregated into player-level quantum centralities and team-level descriptors. In the supplied results, a random forest using fuzzy-quantum descriptors obtained a macro-AUC of 0.551, compared with 0.525 for a classical-centrality baseline, although its accuracy was lower. A
World Cup Final case study ranked Paul Pogba highest among France players by the proposed structural centrality. These findings are exploratory: the attached source package contains neither executable analysis code nor fold assignments, so the reported predictive metrics require independent reproduction with match-grouped validation before publication. The framework is therefore presented primarily as an interpretable player-influence model, with outcome prediction as a preliminary application.

Keywords:

Continuous-time quantumwalk, Fuzzy graph, Multilayer network, Football analytics, Quantum centrality, StatsBomb

References

  1. [1] Grund, T. U. (2012). Network structure and team performance: The case of English Premier League soccer teams. Social networks, 34(4), 682-690. https://doi.org/10.1016/j.socnet.2012.08.004
  2. [2] Pena, J. L., & Touchette, H. (2012). A network theory analysis of football strategies. https://doi.org/10.48550/arXiv.1206.6904
  3. [3] Clemente, F. M., Martins, F. M. L., & Mendes, R. S. (2016). Social network analysis applied to team sports analysis. Springer. https://doi.org/10.1007/978-3-319-25855-3
  4. [4] Buldú, J. M., Busquets, J., Echegoyen, I., & Seirul. lo, F. (2019). Defining a historic football team: Using network science to analyze Guardiola’s FC Barcelona. Scientific reports, 9(1), 13602. https://doi.org/10.1038/s41598-019-49969-2
  5. [5] Buldú, J. M., Busquets, J., Martínez, J. H., Herrera-Diestra, J. L., Echegoyen, I., Galeano, J., & Luque, J. (2018). Using network science to analyse football passing networks: Dynamics, space, time, and the multilayer nature of the game. Frontiers in psychology, 9, 1900. https://doi.org/10.3389/fpsyg.2018.01900
  6. [6] Farhi, E., & Gutmann, S. (1998). Quantum computation and decision trees. Physical Review A, 58(2), 915. https://doi.org/10.1103/PhysRevA.58.915
  7. [7] Childs, A. M. (2009). Universal computation by quantum walk. Physical review letters, 102(18), 180501. https://doi.org/10.1103/PhysRevLett.102.180501
  8. [8] Izaac, J. A., Zhan, X., Bian, Z., Wang, K., Li, J., Wang, J. B., & Xue, P. (2017). Centrality measure based on continuous-time quantum walks and experimental realization. Physical review A, 95(3), 032318. https://doi.org/10.1103/PhysRevA.95.032318
  9. [9] Rossi, L., Torsello, A., & Hancock, E. R. (2014). Node centrality for continuous-time quantum walks. Joint IAPR international workshops on statistical techniques in pattern recognition (SPR) and structural and syntactic pattern recognition (SSPR) (pp. 103-112). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-44415-3_11
  10. [10] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  11. [11] Rosenfeld, A. (1975). Fuzzy graphs. In Fuzzy sets and their applications to cognitive and decision processes (pp. 77-95). Academic Press. https://doi.org/10.1016/B978-0-12-775260-0.50008-6
  12. [12] Tavana, M., Azizi, F., Azizi, F., & Behzadian, M. (2013). A fuzzy inference system with application to player selection and team formation in multi-player sports. Sport management review, 16(1), 97-110. https://doi.org/10.1016/j.smr.2012.06.002
  13. [13] Duch, J., Waitzman, J. S., & Amaral, L. A. N. (2010). Quantifying the performance of individual players in a team activity. PloS one, 5(6), e10937. https://doi.org/10.1371/journal.pone.0010937
  14. [14] Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of complex networks, 2(3), 203-271. https://doi.org/10.1093/comnet/cnu016
  15. [15] Holme, P., & Saramäki, J. (2012). Temporal networks. Physics reports, 519(3), 97-125. https://doi.org/10.1016/j.physrep.2012.03.001
  16. [16] Ramos, J., Lopes, R. J., & Araújo, D. (2018). What’s next in complex networks? Capturing the concept of attacking play in invasive team sports. Sports medicine, 48(1), 17-28. https://doi.org/10.1007/s40279-017-0786-z
  17. [17] StatsBomb. (2025). StatsBomb open data [GitHub repository]. https://github.com/statsbomb/open-data.

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Published

2025-09-17

Issue

Vol. 1 No. 3 (2025): Transactions on Soft Computing

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Articles

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How to Cite

Kuity, N., & Sahoo, L. (2025). Temporal Multilayer Fuzzy Quantum Graphs for Football Outcome Prediction and Player-Influence Ranking. Transactions on Soft Computing , 1(3), 203-216. https://doi.org/10.48314/tsc.v1i3.69