Collaboration Graph - Collaboration Distance

The distance between two people/nodes in a collaboration graph is called the collaboration distance. Thus the collaboration distance between two distinct nodes is equal to the smallest number of edges in an edge-path connecting them. If no path connecting two nodes in a collaboration graph exists, the collaboration distance between them is said to be infinite.

The collaboration distance may be used, for instance, for evaluating the citations of an author, a group of authors or a journal.

In the collaboration graph of mathematicians, the collaboration distance from a particular person to Paul Erdős is called the Erdős number of that person. MathSciNet has a free online tool for computing the collaboration distance between any two mathematicians as well as the Erdős number of a mathematician. This tool also shows the actual chain of co-authors that realizes the collaboration distance.

For the Hollywood graph, an analog of the Erdős number, called the Bacon number, has also been considered, which measures the collaboration distance to Kevin Bacon.