A converse of Tellegen´s theorem

Let N and N˜ be directed networks having the same number of branches labeled correspondingly. The main result is that if u^T i˜=i^Tu˜ for all vectors of corresponding branch voltages u, u˜ and currents i,i˜ satisfying Kirchhoff´s voltage and current laws in every loop and cutset of N and N, then under imposed correspondence of branches the networks are 2-isomorphic. This establishes the converse to Tellegen´s famous theorem