On the Robustness of Cascade Diffusion under Node Attacks

Abstract

How can we assess a network’s ability to maintain its functionality under attacks? Network robustness has been studied extensively in the case of deterministic networks. However, applications such as online information diffusion and the behavior of networked public raise a question of robustness in probabilistic networks. We propose three novel robustness measures for networks hosting a diffusion under the Independent Cascade (IC) model, susceptible to node attacks. The outcome of such a process depends on the selection of its initiators, or seeds, by the seeder, as well as on two factors outside the seeder’s discretion: the attack strategy and the probabilistic diffusion outcome. We consider three levels of seeder awareness regarding these two uncontrolled factors, and evaluate the network’s viability aggregated over all possible extents of node attacks. We introduce novel algorithms from building blocks found in previous works to evaluate the proposed measures. A thorough experimental study with synthetic and real, scale-free and homogeneous networks establishes that these algorithms are effective and efficient, while the proposed measures highlight differences among networks in terms of robustness and the surprise they furnish when attacked. Last, we devise a new measure of diffusion entropy that can inform the design of probabilistically robust networks.