## Erdős number

Erdős number is a positive integer which shows the “distance” from Paul Erdős in publication sense. An author's Erdős number is 1 if he has co-authored a paper with Erdős. 2 if he has co-authored a paper with someone whose Erdős number is 1, but has not with Erdős. And so on: anybody’s Erdős number is `k+1`, if `k` is the lowest number among his/her co-authors’ Erdős numbers.

In other words we can define a graph where vertices are authors, and there is an edge between two authors if and only if they have a common paper. (It is called collaboration graph.) Erdős number of an author is the length of a shortest path (distance) between Erdős and the author in this graph.

Erdős authored more than 1500 papers and worked with more than 500 collaborators. (Therefore more than 500 people's Erdős number is 1.)

The Erdős Webgraph Project does not investigate the properties of Erdős numbers and does not collect data about collaboration graph.

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