Let N and N be directed networks having the same number of branches labelled correspondingly. It is proved that one of them can be reorientated so that u~T i = i~T u for all vectors of corresponding branch voltages u, u-bar and currents i, i-bar satisfying Kirchhoff's voltage and current law in every loop and cutset of N and N-bar if and only if under imposed correspondence of branches the networks are 2-isomoprhic. This is an 'if and only if' version of the converse of Tellegen's famous theorem established recently by the author and shows that Tellegen's theorem can in general be formulated for 2-isomorphic networks.
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