Universal relation for transport in non-sparse complex networks

Transport properties of a complex network can be reflected by the two-point resistance between any pair of two nodes. We systematically investigate a variety of typical complex networks encountered in nature and technology, in which we assume each link has unit resistance, and we find for non-sparse network connections a universal relation exists that the two-point resistance is equal to the sum of the inverse degree of two nodes up to a constant. We interpret our observations by the localization property of the network’s Laplacian eigenvectors. The findings in this work can possibly be applied to probe transport properties of general non-sparse complex networks.