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"Quiver" is the word used for "directed graph" in some parts of representation theory. The main reason to use the term quiver is to indicate an interest in considering representations of the quiver.
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Matrices into path algebras
The reason I say this is because this perspective allows you to realize a lot of other quivers as subalgebras of matrices, and vice versa (for instance, the Borel subalgebra as the path algebra of a subquiver … It's not an extremely useful proving technique, but it can be a good way to produce a lot of quivers, especially when first learning about them.
Is it interesting? …