If $f$ is a map from a finite set to itself, is there any widely accepted definition of the "degree" of $f$?
I would like to define deg $f$ as the quantity discussed in Quantifying the noninvertibility of a function since this aligns nicely with both the notion of degree used in graph theory (specifically, consider the root-mean-square indegree of the functional digraph of $f$) and the notion of degree used in complex dynamics (a map of degree $d$ is $d$-to-one almost everywhere). But I don't want my definition to collide with something that already exists and is in common use in combinatorics.
