Enhanced predictability of hierarchical propagation in complex networks

We apply recent results on the dynamics of random walkers to the analysis of idealized epidemic outbreaks in scale-free networks. By replacing the node degree with the random walk centrality (RWC) we observe a refined hierarchical cascade leading to a greatly enhanced predictability for the order of infected nodes. We confirm our model results on data from real-world Internet maps at the autonomous system level. In addition we propose the RWC distribution as an additional relevant topological property of a complex network. The present results are highly relevant for the understanding of information flow in scale-free networks and the development of dynamic and adaptive strategies that aim to mitigate network attacks.