A network model for the representation of the general 3-dimensional electromagnetic field has been presented in previous publications. Solution of the network was performed by an all mesh variable method. A method is described in the paper for the solution of the linked network model in terms of a scalar potential in the magnetic part of the field, and the mesh currents in the electric part. The validity of the solution method is confirmed by a comparison of calculations with experimental results, for a full 3-dimensional problem. The new node-mesh method is shown to give rise to considerably less variables than the all mesh variable method for the solution of the linked-network problem. A comparison is also made between the number of variables required by the node-mesh method and that required by some other differential equation formulations of the 3-dimensional eddy-current problem.