Erdős Number and Small World Phenomenon
The word “small‐world phenomenon” represents highly clustered networks in modern days. The world is indeed small from the viewpoint of dynamic network systems that connect random people. Also closely related to the famous “six degrees of separation,” the theory that everyone is connected at most six steps away from each other, the shrinking world via various linkages became an interest for scholars. This marvelous fact that any two random people are related by a consecutive chain of “friends of friends” was proposed in different form using the Erdos number, an idea introduced by a famous Hungarian Mathematician Paul Erdos.
Collaborating with more than 500 co-researchers, Paul Erdos himself was in the center of network among his scholars. He defined Erdos number in the following way:
I) Erdos himself has Erdos number 0
II) People who had direct collaboration with Erdos himself has Erdos number 1
III) People who collaborated with the subgroup of Erdos number k has Erdos number k+1
The number measures the distance from Erdos, so that the smaller Erdos number implies close relationship with Erdos. Therefore, Erdos number was the criterion for scholars to find out the degree of collaboration. In fact, many Nobel laureates were having Erdos number less than 5, which shows how they were linked to Erdos as well as other scholars. Mathematicians, noticing the importance of the network, modelled it with collaboration graph, where two people are joined by edge as they collaborate. According to the graph, among working mathematicians, Erdos number ranges up to 15, with median 5. This definitely shows how small-world phenomenon dominates academia in its network.
Link: http://www.oakland.edu/enp/
Reference Video: http://www.yovisto.com/video/20504