Structural robustness of scale-free networks against overload failures.

We study the structural robustness of scale-free networks against overload failures induced by loads exceeding the node capacity, based on analytical and numerical approaches to the percolation problem in which a fixed number of nodes are removed according to the overload probability. Modeling fluctuating loads by random walkers in a network, we find that the degree dependence of the overload probability drastically changes with respect to the total load. We also elucidate that there exist two types of structural robustness of networks against overload failures. One is measured by the critical total load W(c) and the other is by the critical node removal fraction f(c). Enhancing the scale-free property, networks become fragile in both senses of W(c) and f(c). By contrast, increasing the node tolerance, scale-free networks become robust in the sense of the critical total load, while they come to be fragile in the sense of the critical node removal fraction. Furthermore, we show that these trends are not affected by degree-degree correlations, although assortative mixing makes networks robust in both senses of W(c) and f(c).