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Quantum networks are natural scenarios for the communication of informationamong distributed parties, and the arena of promising schemes for distributedquantum computation. Measurement-based quantum computing is a prominent exampleof how quantum networking, embodied by the generation of a special class ofmultipartite states called cluster states, can be used to achieve a powerfulparadigm for quantum information processing. Here we analyze randomly generatedcluster states in order to address the emergence of multipartite correlationsas a function of the density of edges in a given underlying graph. We find thatthe most widespread multipartite entanglement does not correspond to thehighest amount of edges in the cluster. We extend the analysis to higherdimensions, finding similar results, which suggest the establishment of smallworld structures in the entanglement sharing of randomised cluster states,which can be exploited in engineering more efficient quantum informationcarriers.

Structure of multipartite entanglement in random cluster-like photonic systems