  When $\Gamma$ is a row-finite di(rected )graph we classify all finite
dimensional modules of the Leavitt path algebra $L(\Gamma)$ via an explicit
Morita equivalence given by an effective combinatorial (reduction) algorithm on
the digraph $\Gamma$. The category of (unital) $L(\Gamma)$-modules is
equivalent to a subcategory of quiver representations of $\Gamma$. However the
category of finite dimensional representations of $L(\Gamma)$ is tame in
contrast to the finite dimensional quiver representations of $\Gamma$ which are
almost always wild.
