\begin{definition}[Definition:Parallel (Matroid)]
Let $M = \struct {S, \mathscr I}$ be a matroid.
Two elements $x, y \in S$ are said to be '''parallel''' in $M$ {{iff}} they are not loops but $\set {x, y}$ is a dependent subset of $S$.
That is, $x, y \in S$ are '''parallel''' {{iff}}:
:$\set x, \set y \in \mathscr I$ and $\set {x, y} \notin \mathscr I$.
\end{definition}