Identifying the Weak Set in Interdependent Networks Considering Cascading Failures

Identifying the weak set of interdependent networks that influences both structure and function is of great importance for studying infrastructure resilience and supporting engineering management. However, the vulnerability of interdependent networks arises not only from their structural properties but also from the cascading propagation of failures, which increases the complexity of weak set identification and makes it difficult for classical methods to balance both accuracy and efficiency. In this study, a data-driven framework, termed the GCN-WSI (Graph Convolutional Network-based Weak Set Identification model), is proposed to identify the weak set that can disintegrate interdependent networks under cascading failures. First, the cascading failure mechanism and related properties of interdependent networks are characterized, which reformulates weak set identification as a prediction problem of estimating the probability that nodes belong to the weak set. Second, the concept of dual-stream graph embedding is introduced to aggregate neighbor information within and across layers, incorporating attributes associated with structural properties and cascading failures to construct comprehensive representations. Finally, a multilayer perceptron (MLP) regressor is employed to estimate the probability of node membership in the weak set. The GCN-WSI framework is trained on small-scale synthetic networks and is applicable to large-scale real-world systems. Experiments on diverse datasets validate the effectiveness of the proposed method and highlight the necessity and feasibility of specific components. In particular, under predefined disintegration targets, the model demonstrates strong capability in identifying a compact weak set whose removal leads to a rapid decline in network performance.