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In this paper we apply the Singular Value Decomposition (SVD) analysis to examining the coupling structure of an electrical power grid in order to highlight opportunities for reducing the network traffic, by identifying what are the salient data that need to be communicated between parts of the infrastructure to apply a control action. Our main finding is that typical grid admittance matrices have singular values and vectors with only a small number of strong components. The SVD sparsity can be exploited to construct an efficient decentralized system-wide monitoring and control architecture. We also discuss the potential applications of the proposed architecture and its robustness under contingency; and experiment the SVD analysis with the NYISO-2935 system and the IEEE-300 system.