Rank National Football Teams with PageRank
Besides its well-known use in search engine, PageRank can be used in other networks as well. Lazova and Basnarkov from Cyril and Methodius University in Macedonia applied PageRank to rank national football teams, based on the World Cup tournaments since 1930. In their model, each national team is a node, and each edge represents a game played between the two nodes, starting from the team that lost and pointing to the team that won. Their ranking result was similar to that of FIFA, despite some differences.
Though not mentioned in the article, there is another aspect that this network of national football teams is very similar to that of webpages – both are not strongly connected. If one team only wins few games, or no games at all, it will have few or no incoming edges; as a result, it is not likely to be able to go to this particular node from other nodes. We need to apply the scaled PageRank update rule in both cases, giving each node some units of free PageRank at the end of the iteration after scaling, to prevent some teams having accumulated value as wrong representation.
It is interesting that PageRank can be used to rank football teams. FIFA’s ranking system basically assigns certain weights and points to teams based on different factors, whereas PageRank looks at the results directly, with the advantage of taking the ability of opponents into account automatically (if one team wins the game, thus having an incoming node from a good team, this team is more likely to be good). From this application, we can conclude that PageRank can be used in the scenarios where we need to rank many agents, who interact among themselves in a relatively random way (i.e. one does not have to interact with everyone else).
Sources: