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Time synchronized measurements of voltage magnitudes or phasors are increasingly common in electrical networks. Voltage measurement statistics are informative of the underlying network structure or topology making them useful for grid monitoring. However, this connection is poorly understood and many proposed voltage analytics are purely heuristic. We use graph theory to establish sound theoretical connections between voltage measurements and the structure of the underlying network. Our results are important for many applications, from topology estimation to missing data recovery. Based on this new theory, we discuss existing analytics, transforming them from heuristic to theoretically justified approaches, and introduce new analytics. We clarify all assumptions made, to indicate when analytics may fail or perform poorly. Our work enables voltage measurement streams to be transformed into physically meaningful, intuitive, visualizable, actionable information through simple algorithms.