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

TL;DR

The paper tackles the NP-hard critical node problem (CNP) in sparse graphs by proposing FGDD, an end-to-end framework that combines a feature importance-aware graph attention network with a dueling double deep Q-network. By formulating CNP as a Markov decision process, FGDD learns robust node representations from initial topology-derived features and sequentially selects nodes to remove, guided by a global reward based on the change in residual connectivity $f(S)$. Experiments on 28 real-world networks show FGDD is competitive with state-of-the-art heuristics and DRL baselines, and its performance can be further boosted via a simple local-search strategy (CBNS). The work demonstrates strong generalization to networks of different sizes and topologies without problem-specific labeling, and it highlights potential extensions to additional graph-structured tasks and applications such as road-network resilience.

Abstract

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.

Figures (3)

• Figure 2: Overview of the FGDD framework. We first take basic metrics for a network as initial features for our graph neural network. These metrics provide a fundamental understanding of the network, especially for synthetic networks without given features. These initial features are concatenated and fed into GAT, which employs self-attention mechanisms that allow nodes to weigh the importance of their neighbors' features. We then have representation in latent space for each node and feed these representations to a reinforcement learning agent. After selecting and removing a certain node, we update the replay memory with state, action, and reward.
• Figure 3: Performance curves of FGDD and baseline methods under different $K$ values. Here we show the pairwise connectivity decreasing trend for each step after removing the selected node.
• Figure 4: Ablation study on real-world networks. We compare our FGDD method with its four variants by removing the feature aggregation (w/o FA) method, variance-constrained GAT (w/o VG) module, and dueling DDQN (w/o DD) module, respectively. In addition, We also report the results of FGDD under a different reward function (FGDD-R for short).