  The robustness of complex networks against node failure and malicious attack
has been of interest for decades, while most of the research has focused on
random attack or hub-targeted attack. In many real-world scenarios, however,
attacks are neither random nor hub-targeted, but localized, where a group of
neighboring nodes in a network are attacked and fail. In this paper we develop
a percolation framework to analytically and numerically study the robustness of
complex networks against such localized attack. In particular, we investigate
this robustness in Erd\H{o}s-R\'{e}nyi networks, random-regular networks, and
scale-free networks. Our results provide insight into how to better protect
networks, enhance cybersecurity, and facilitate the design of more robust
infrastructures.
