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This paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and transformers. Such networks admit a symmetric formulation of their circuit equations. We introduce SyPVL, an efficient and numerically stable algorithm for the computation of reduced-order models of large, linear, passive networks. SyPVL represents the specialization of the more general PVL algorithm, to symmetric problems. Besides the gain in efficiency over PVL, SyPVL also preserves the symmetry of the problem, and, as a consequence, can often guarantee the stability of the resulting reduced-order models. Moreover, these reduced-order models can be synthesized as actual physical circuits, thus facilitating compatibility with existing analysis tools. The application of SyPVL is illustrated with two interconnect-analysis examples.