Let $G = (V,E)$ be a finite graph, allowing loops and parallel edges, and let $e \in E$. Let $M(G)$ denote the graphic matroid on ground set $E$, whose independent sets are precisely the edge subsets $F \subset E$ such that the spanning subgraph $(V,F)$ is a forest. Then, under the natural identification of ground sets with $E \setminus \{e\}$,

\begin{align*} M(G) \setminus e = M(G \setminus e). \end{align*}

Moreover,

\begin{align*} M(G) / e = M(G / e), \end{align*}

where, if $e$ is a loop edge of $G$, the graph contraction $G/e$ is interpreted as $G \setminus e$, matching the matroid convention that contracting a loop has the same effect as deleting it.