  The present paper is concerned with the concept of the one-way quantum
computer, beyond binary-systems, and its relation to the concept of stabilizer
quantum codes. This relation is exploited to analyze a particular class of
quantum algorithms, called graph algorithms, which correspond in the binary
case to the Clifford group part of a network and which can efficiently be
implemented on a one-way quantum computer. These algorithms can ``completely be
solved" in the sense that the manipulation of quantum states in each step can
be computed explicitly. Graph algorithms are precisely those which implement
encoding schemes for graph codes. Starting from a given initial graph, which
represents the underlying resource of multipartite entanglement, each step of
the algorithm is related to a explicit transformation on the graph.
