Supercurrents in networks with constricted junctions

We consider a system of superconducting networks with constrictions in the junctions. It is argued that for a family of canonical scalings of the junction size the network can be modeled by a deGennes-Alexander energy functional plus an extra term that depends on the jump of the order parameter across the junction. The current equations for such junctions are a natural generalization of the Josephson condition for a standard weak link in a wire. The model is solved for a number of special network geometries.