Identification of current-carrying part of a random resistor network: electrical approaches vs. graph theory algorithms

A set of current-carrying bonds of a random resistor network (RRN) is called the (effective) backbone. The (geometrical) backbone can be defined as a union of all self-avoiding walks between two given points on a network or between its opposite borders. These two definitions provide two different approaches for identification of backbones. On the one hand, one can treat an arbitrary network as RRN and calculate potentials and currents in this RRN. On the other hand, one can apply to the network some search algorithms on graphs. Each of these approaches are known to have both advantages and drawbacks. We have implemented several different algorithms for backbone identification. The algorithms were applied to backbone identification for different system sizes and concentrations of conducting bonds. Our analysis suggests that a universal algorithm suitable for any problem is hardly possible to offer. Most likely, each particular task needs a specific algorithm.