A converse of Tellegen's theorem

Let N and N/spl tilde/ be directed networks having the same number of branches labeled correspondingly. The main result is that if u/sup T/i/spl tilde/=i/sup T/u/spl tilde/ for all vectors of corresponding branch voltages u, u/spl tilde/ and currents i,i/spl tilde/ 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.