Definition:Parallel (Matroid)

Definition
Let $M = \struct{S, \mathscr I}$ be a matroid.

Two elements $x, y \in S$ are said to be parallel in $M$ If they are not loops but $\set{x,y}$ is a dependent subset of $S$.

That is, $x, y \in S$ are parallel if:
 * $\set x, \set y \in \mathscr I$ and $\set{x, y} \not \in \mathscr I$.