Persistent currents on networks

We develop a method to calculate persistent currents and their spatial dist ribution (and transport properties) on graphs made of quasi-1D diffusive wi res. They are directly related to the held derivatives of the determinant o f a matrix which describes the topology of the graph. In certain limits, th ey are obtained by simple counting of the nodes and their connectivity. We relate the average current of a disordered graph with interactions and the noninteracting current of the same graph with clean 1D wires. A similar rel ation exists for orbital magnetism in general. [S0031-9007(99)09102-4].