Learning to Detect Critical Nodes in Sparse Graphs via Feature Importance Awareness

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.
Note to Practitioners
—This work is motivated by the problems of identifying influential nodes from a sparse graph or network. Various practical applications can be naturally modeled as critical node problems, e.g., finding the most influential stations or airports within a transportation network, identifying a specific number of people to be vaccinated in order to reduce the overall transmissibility of a virus, and reinforcing the protection over some most important nodes to make the electric network more stable. It proposes an effective end-to-end deep learning algorithm to solve the critical node problem. The proposed approach combines feature importance-aware graph attention network with dueling double deep Q-network. Extensive numerical experiments and comparisons show that our proposed algorithm is highly comparable to state-of-the-art algorithms and can help decision-makers to discover valuable knowledge or influential nodes in a real-world network.