The above graph G is a very small part of Paul Erdös graph, whose vertices are the mathematicians and edges are connected by a joint publication. Every mathematician has a finite or infinite lenght of path to Erdös. This number is named your Erdös number. The valency of the graph, highest degree of a vertex, is 507 in Paul Erdös or say those lucky people whose Erdös number is 1. To find out where you are in G, check the site Erdös Number Project you may be closer than you thought, as it happened to me. The graph also shows my co-authors, neighbouring vertices of Oruç and hence d(Oruç)=3 which is also the distance between P.Erdös and H.Oruç.