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This quiver has one vertex and $r$ loops. Paths are words in the loops, so its path algebra is a free associative algebra. A representation assigns an arbitrary endomorphism to each loop.

This quiver has $r$ source vertices, each with one arrow to a common sink. Its path algebra has the vertex idempotents and the arrows as basis. After extracting source kernels from a representation, its remaining arrows identify the source spaces with subspaces of the sink.