\begin{definition}[Definition:Cycle Matroid]
Let $G$ be a graph.
Let $E$ be the edge set of $G$.
Let $\mathscr I$ be the set of edge sets of subgraphs of $G$ that contain no cycles.
Then the ordered pair $\struct{E, \mathscr I}$ is called the '''cycle matroid''' of the graph $G$.
\end{definition}