Abstract: Graph states-multipartite entangled states that can be represented by mathematical graphs-are important resources for quantum computation, quantum error correction, studies of multiparticle entanglement and fundamental tests of non-locality and decoherence. Here, we demonstrate the experimental entanglement of six photons and engineering of multiqubit graph states. We have created two important examples of graph states, a six-photon Greenberger-Horne-Zeilinger state, the largest photonic Schrödinger cat so far, and a six-photon cluster state, a state-of-the-art `one-way quantum computer'. With small modifications, our method allows us, in principle, to create various further graph states, and therefore could open the way to experimental tests of, for example, quantum algorithms or loss- and fault-tolerant one-way quantum computation.