  We develop a method to calculate the persistent currents and their spatial
distribution (and transport properties) on graphs made of quasi-1D diffusive
wires. They are directly related to the field derivatives of the determinant of
a matrix which describes the topology of the graph. In certain limits, they are
obtained by simple counting of the nodes and their connectivity. We relate the
average current of a disordered graph with interactions and the non-interacting
current of the same graph with clean 1D wires. A similar relation exists for
orbital magnetism in general.
