Maps of Tournaments: Distances, Experiments, and Data

2026-01-26

European Conference on Artificial Intelligence

AI Summary

This study addresses the challenge of effectively measuring and visualizing structural differences among tournaments. To this end, tournaments are modeled as complete directed graphs, and a novel distance metric tailored to tournament structures is introduced. For the first time in this domain, the election map framework is adapted to embed tournaments into a two-dimensional Euclidean space, where pairwise distances reflect their structural dissimilarities. By combining synthetic tournaments generated stochastically with real-world data, the proposed approach yields an intuitive and interpretable “tournament map,” enabling meaningful comparison and analysis of both synthetic and empirical tournament structures.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We form a"map of tournaments"by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no ties allowed). A map is a set of tournaments represented as points on a 2D plane, so that their Euclidean distances resemble the distances computed according to a given measure. We identify useful distance measures, discuss ways of generating random tournaments (and compare them to several real-life ones), and show how the maps are helpful in visualizing experimental results (also for knockout tournaments).

Problem

• tournament
• map
• distance measure
• visualization
• graph representation

Innovation

• tournament map
• distance measure
• random tournament generation
• visualization
• knockout tournament