Volume 51, Number 4, October-December 2017
|Page(s)||1055 - 1076|
|Published online||24 November 2017|
The vertex attack tolerance of complex networks
Southern Illinois University, Edwardsville, Illinois, USA.
Received: 19 May 2016
Accepted: 27 January 2017
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.
Mathematics Subject Classification: 68R10 / 90B15 / 05C50 / 68Q25
Key words: Graph theory / resilience / Scale-Free networks / spectral Gap / approximation Hardness / Heuristic Algorithms
© EDP Sciences, ROADEF, SMAI 2017
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.