  We construct some irreducible representations of the Leavitt path algebra of
an arbitrary quiver. The constructed representations are associated to certain
algebraic branching systems. For a row-finite quiver, we classify algebraic
branching systems, to which irreducible representations of the Leavitt path
algebra are associated. For a certain quiver, we obtain a faithful completely
reducible representation of the Leavitt path algebra. The twisted
representations of the constructed ones under the scaling action are studied.
