Let $U \subset \mathbb R^n$ be open. The set $U$ is the graph of a some function if for all $x \in U$, there exists unique $y \in \mathbb R^m$ such that $(x,y) \in A$.
Alternatively, let $f:A\to B$ be a set function. The set \(\Gamma = \{(a,b) \in A\times B \mid b=f(a)\}\) is the graph of $f$.
Wikidata ID: Q182598