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Positive definiteness conditions on the conductance, capacitance and inductance matrices are replaced by certain algebraic assumptions on the so\u2010calledproper trees<\/jats:italic>for augmented node analysis andnormal trees<\/jats:italic>for modified node analysis. The current discussion is restricted to index\u20100 and index\u20101 systems; for the latter, the analysis is based upon certain matrix factorizations which split the topological information from the electrical features of the devices. Several examples illustrate the scope of our framework. 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