` : Erdos did a lot of work in Graph Theory generally; the Erdos-Spencer Probailistic Method is conspicuous but not particularly pertinent to Erdos Numbers. Erdos coauthored with a huge number of people (500 odd). If you consider the graph G with E set defined by (x,y) in E when x coauthors with y, then Erdos is the highest degree node in the largest connected component. That makes him a natural ``root`` node to designate.  `