There are also Morphy numbers - chessmaster Paul Morphy had Morphy Number 0. If you played a game with Morphy, you have Morphy number 1, etc. The sum of Erdos number and Morphy number was discussed on a chess newsgroup about a year ago.

On Tuesday 13 December 2005 17:48, Jud McCranie wrote:

There are also Morphy numbers - chessmaster Paul Morphy had Morphy Number 0. If you played a game with Morphy, you have Morphy number 1, etc. The sum of Erdos number and Morphy number was discussed on a chess newsgroup about a year ago.

Seems to me that here you might want some sort of weighting where you get "charged" less for a connection when you won the game. (Maybe the charges should be parameterized by rating so that, given the typical distribution of games in the career of a player of given rating, your expected cost-of-direct-connection with another player is independent of the ratings, or something.) After all, there must be fewer people who beat someone who beat someone who beat someone who beat Morphy than people who were beaten by someone who was beaten by someone who was beaten by someone who was beaten by Morphy. -- g