In graph theory, the indegree of a vertice $v$ in a directed graph is denoted as $\deg^{-} v$ (or $\deg_{-} v$ in some books), and outdegree of $v$ is denoted as $\deg^{+} v$ (or $\deg_{+} v$, similarly). Why use $-$ for $in$ and $+$ for $out$? Isn't that counterintuitive? Any resources explaining that?
[Math] Graph theory: indegree and outdegree notation
directed graphsgraph theory
Best Answer
I think it comes from vector calculus. For a surface (manifold, even), we usually call the outward pointing normal the positive orientation, and the inward normal negative. So, outdegree gets associated with a plus sign and indegree a minus.