Replace every original edge by two edges meeting at a new two-port equality vertex. Put all old vertices on one side and all new equality vertices on the other. This makes the graph bipartite. Each old wire value has exactly one allowed pair of new bits, (0,0) or (1,1); unequal pairs contribute zero. Therefore the contraction is unchanged. Every old vertex keeps its degree; each new vertex has degree two. The number of wires doubles. Treat parallel original wires separately, preserving their port identities.