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We propose a new approach for static translinear network synthesis. We model the network topology in terms of graph theory, leading to a catalog of valid translinear networks. The catalog serves as a synthesis tool for circuits with given desired input-output behavior. Methods from algebraic geometry and computer algebra are used to match the desired behavior with the models from the catalog, turning our approach into a powerful synthesis tool for analog circuits. The strategy is applied successfully to new circuits for industrial use.