  Detecting critical nodes in sparse graphs is important in a variety of
application domains, such as network vulnerability assessment, epidemic
control, and drug design. The critical node problem (CNP) aims to find a set of
critical nodes from a network whose deletion maximally degrades the pairwise
connectivity of the residual network. Due to its general NP-hard nature,
state-of-the-art CNP solutions are based on heuristic approaches. Domain
knowledge and trial-and-error are usually required when designing such
approaches, thus consuming considerable effort and time. This work proposes a
feature importance-aware graph attention network for node representation and
combines it with dueling double deep Q-network to create an end-to-end
algorithm to solve CNP for the first time. It does not need any
problem-specific knowledge or labeled datasets as required by most of existing
methods. Once the model is trained, it can be generalized to cope with various
types of CNPs (with different sizes and topological structures) without
re-training. Computational experiments on 28 real-world networks show that the
proposed method is highly comparable to state-of-the-art methods. It does not
require any problem-specific knowledge and, hence, can be applicable to many
applications including those impossible ones by using the existing approaches.
It can be combined with some local search methods to further improve its
solution quality. Extensive comparison results are given to show its
effectiveness in solving CNP.
