  Complex networks structures have been extensively used for describing complex
natural and technological systems, like the Internet or social networks. More
recently complex network theory has been applied to quantum systems, where
complex network topologies may emerge in multiparty quantum states and quantum
algorithms have been studied in complex graph structures. In this work we study
multimode Continuous Variables entangled states, named cluster states, where
the entanglement structure is arranged in typical real-world complex networks
shapes. Cluster states are a resource for measurement-based quantum information
protocols, where the quality of a cluster is assessed in term of the minimal
amount of noise it introduces in the computation. We study optimal graph states
that can be obtained with experimentally realistic quantum resources, when
optimized via analytical procedure. We show that denser and regular graphs
allow for better optimization. In the spirit of quantum routing we also show
the reshaping of entanglement connections in small networks via linear optics
operations based on numerical optimization.
