The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into larger networks. It is an open question to what degree modularity also holds for quantum circuits -- circuits made of superconducting material, in which electric voltages and currents are governed by the laws of quantum physics. If realizable, quantum coherence in larger circuit networks has great potential for advances in quantum information processing including topological protection from decoherence. Here, we present theory suitable for quantitative modeling of such large circuits and discuss its application to the fluxonium device. Our approach makes use of approximate symmetries exhibited by the circuit, and enables us to obtain new predictions for the energy spectrum of the fluxonium device which can be tested with current experimental technology.