Electrical Transport in Small-World Networks

In this work, we study the characteristic of the electrical transport in small-world resistor networks where the resistance is considered as a power law function of the distance between two connected nodes. By Monte Carlo´s method. We study the effects of shortcuts probability on the average resistance and its standard deviation of the small-world resistor networks, and the relation between the power-law exponent and the average resistance and its standard deviation. We find all properties rapidly decay to the case of the random resistor network for an arbitrarily small density of shortcuts and the average resistance and its standard deviation increase with the power-law exponent. For all these results, the reasonable explanation is given.