The vertex attack tolerance of complex networks

The purpose of this work is four-fold: (1) We propose a new measure of network resilience in the face of targeted node attacks, vertex attack tolerance , represented mathematically as , and prove that for d -regular graphs τ (G ) = Θ (Φ (G )) where Φ (G ) denotes conductance, yielding spectral bounds as corollaries. (2) We systematically compare τ (G ) to known resilience notions, including integrity, tenacity, and toughness, and evidence the dominant applicability of τ for arbitrary degree graphs. (3) We explore the computability of τ , first by establishing the hardness of approximating unsmoothened vertex attack tolerance under various plausible computational complexity assumptions, and then by presenting empirical results on the performance of a betweenness centrality based heuristic algorithm applied not only to τ but several other hard resilience measures as well. (4) Applying our algorithm, we find that the random scale-free network model is more resilient than the Barabasi−Albert preferential attachment model, with respect to all resilience measures considered.