A proof of the generalized topological Kirchhoff´s rules

Kirchhoff´s topological rules for linear reciprocal networks have been generalized for networks containing non-reciprocal elements as well, in order to be applicable to active networks. A conventional proof of these rules for reciprocal networks is given, and the generalized rules are then shown to be an immediate consequence of this proof, thus requiring no special considerations for their derivation. The exposition is restricted to nodal analysis.