Definition:Parallel (Matroid)

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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 and only if:

$\set x, \set y \in \mathscr I$ and $\set {x, y} \notin \mathscr I$.