On the Robustness of Diffusion in a Network Under Node Attacks

Alvis Logins, Yuchen Li, Panagiotis Karras

Abstract: How can we assess a network's ability to maintain its functionality under attacks? <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Network robustness</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">probabilistic</i> networks. We propose three novel robustness measures for networks hosting a diffusion under the Independent Cascade or Linear Threshold model, susceptible to attacks by an adversarial attacker who disables nodes. The outcome of such a process depends on the selection of its initiators, or seeds, by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">seeder</i> , as well as on two factors outside the seeder's discretion: the attacker's strategy and the probabilistic diffusion outcome. We consider three levels of seeder awareness regarding these two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uncontrolled</i> factors, and evaluate the network's viability aggregated over all possible extents of an attack. 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, and devise ways to enhance the robustness of probabilistic networks.