Edge boundary in a graph
= Edge boundary in a graph
{title2=$\partial_eA$}
The edge boundary of a vertex set $A$ consists of graph edges with exactly one endpoint in $A$. In a $d$-regular graph,
$$
|\partial_eA|=d|A|-2e(A),
$$
where $e(A)$ counts edges with both endpoints in $A$.
= Edge boundary
{synonym}