Erdős number is an index to describe through how many “steps of collaboration” for a scientist to reach the most prolific mathematician, Paul Erdős. For example, if person A had directly written a paper with Erdős, A’s Erdős number is 1; if person B doesn’t have common paper with Erdős, but B co-wrote a paper with C, and C had co-worked paper with Erdős, then B’s Erdős number is 2; Erdős himself has Erdős number of 0. More info: Erdős number on Wikipedia.
Migrating this logic to osu!, the osu! Erdős number describes how many collaborations one mapper takes to reach to the mapper with the most participated beatmap sets in any given mode.
This idea was raised by osu! Nomination Assessment Team member, Mafumafu (A.K.A. Regraz), in this X tweet of his.