We show that the random-resistor-network problem can be mapped on to a related network of Hooke springs of natural length zero stretched on a frame. The conductance of the network is equivalent to the pressure on the frame. The new viewpoint leads to a useful visualization of conductivity on random networks. The mapping can also be used on tight-binding Hamiltonians. We use this method to study the conductivity and superconductivity of random networks in two dimensions.

• Received 20 April 1987

DOI:https://doi.org/10.1103/PhysRevB.36.3798