http://xxx.lanl.gov/abs/cond-mat/0409609
(click on the PDF link at the bottom for full text)

Having played soccer for a majority of my life, I’d like to think I know everything there is to know about the sport. Though this may be true about the rules and strategies of the game, after the reading the Palacios-Huerta paper I found a new lens with which to look through when analyzing soccer. This academic view that utilizes the world’s most popular sport for game theory applications is also being used to illustrate some interesting relationships found in social networks, namely those amongst players from various clubs. In their paper, Roberto Onody and Paulo Castro study what they call, the “Brazilian soccer network.”

This fairly simple network is composed of a bipartite network that contains two types of vertices; one set is created from the 127 different Brazilian soccer clubs and the other set is created from the 13,411 soccer players who have played for those clubs between the years 1971 and 2002. Much like the networks studied in class, edges are formed based on a social connection. In this network, “whenever a soccer player has been employed by a certain club” they are connected by an edge. Throughout their short but very analytical paper, these two researchers explore a number of relationships and then apply mathematical models to their results. For instance, they found that the probability, P(N), that a player has worked for N clubs follows an exponential decay model, a result of which shows that “it is 190 times more probable to find someone who has played for only two clubs than for eight clubs.”

Subsequently in the paper, the researchers create a “unipartite network composed exclusively by the soccer players. If two players were at the same team at the same time, then they will be connected by an edge.” From this network, they analyze a number of variables that are relevant to our class including the number of edges formed and the average shortest path length between players. With regards to the average shortest path length, they found that within the Brazilian soccer player (BSP) network the value was 3.29. “In analogy with social networks, we can say that there is 3.29 degrees of separation between the Brazilian soccer players, or, in other words, the BSP network is a small-world.”

Onody and Castro leave the reader with some interesting thoughts about their results, postulating as to why such results were found. For example, they think that the “player’s professional life is turning longer and or/ the players transfer rate between teams is growing up.” Lastly, they hope to stimulate further research in the subject, asking whether their results would “hold for soccer players from different countries or, perhaps, different sports.”

In the paper, there were a few variables and relationships that were discussed that I would appreciate knowing a bit more about, namely the “clustering coefficient” and the “assortativity coefficient”. Though the clustering coefficient has been touched upon, perhaps if there is enough time in the course we could review these “relevant parameters in social networks.”