  In this paper we show a new technique to analyze families of rankings. In
particular we focus on sports rankings and, more precisely, on soccer leagues.
We consider that two teams compete when they change their relative positions in
consecutive rankings. This allows to define a graph by linking teams that
compete. We show how to use some structural properties of this competitivity
graph to measure to what extend the teams in a league compete. These structural
properties are the mean degree, the mean strength and the clustering
coefficient. We give a generalization of the Kendall's correlation coefficient
to more than two rankings. We also show how to make a dynamic analysis of a
league and how to compare different leagues. We apply this technique to analyze
the four major European soccer leagues: Bundesliga, Italian Lega, Spanish Liga,
and Premier League. We compare our results with the classical analysis of sport
ranking based on measures of competitive balance.
