FIFA World Cup referees’ networks: a constant-size clique approach

Soccer is a worldwide sport. Every 4 years since 1930, the sport stimulates a growing number of people, countries, and money during the Soccer World Cup. This scientific treatment of matches using complex networks and social networks focuses on the teams participating in the tournaments, as well as on the interaction between players. The present work aims to broaden the scope of studies focusing on referees’ networks. For this purpose, we built referees’ networks of all World Cup competitions to date. We used indices based on the clique approach for the analyses and characterization of the networks, and the detection of clusters was investigated by identifying communities and islands. Some important results emerge from this study, such as the finding that the networks do not follow a pattern throughout their editions with respect to the indices and the structure. There is, however, a change in procedures from the 2006 World Cup with respect to referee choice. This change leads to the emergence of a pattern in the last four World Cups.