Brazilian Soccer – A Small World
One of the most interesting things about networks is the small world phenomenon. This idea can be seen all over the world, and one of the most famous titles given to it was the six degrees of separation. A limiting factor of the 6 degrees is that it doesn’t always apply to smaller sub groups. One of those groups is Brazilian professional soccer players. For this group, they have a much smaller degree of separation than normal. This degree is calculated by assigning each player who played on the same team an edge. After examining this network, the average degree of separation was 3.29. This indicates exactly how much of a small world there is between Brazilian soccer players. However, this hasn’t always been true.
Brazilian soccer didn’t have the same following and resources that it has now. In the past the degree of separation was larger, because teams spent less and transfers occurred less. With the increase in popularity because of widespread communication channels, Brazilian soccer has gained a larger fan base, which continues to contribute more and more money to clubs. This means that they will be able to spend more and more; however, there will most likely be a degree of separation that is a limiting value. This is because there will always be rivalries between clubs who don’t want to trade or buy another club’s player.
An interesting parallel could be drawn from this network – is there a Kevin Bacon or Erdos number for soccer players? It seems in any smaller specific network, there can be a figure such as Bacon or Erdos who seems to have known everyone. Every few years, an older player (who has likely played for multiple teams) could be used to determine a respective degree of separation between him and every other player. Coincidentally, this small world phenomenon probably applies to all major professional soccer leagues. However, you don’t have to be an expert in networks to see it, just a dedicated fan.
http://pre.aps.org/pdf/PRE/v70/i3/e037103