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Multi-Label Continual Learning (MLCL) builds a class-incremental framework in a sequential multi-label image recognition data stream. The critical challenges of MLCL are the construction of label relationships on past-missing and future-missing partial labels of training data and the catastrophic forgetting on old classes, resulting in poor generalization. To solve the problems, the study proposes an Augmented Graph Convolutional Network (AGCN++) that can construct the cross-task label relationships in MLCL and sustain catastrophic forgetting. First, we build an Augmented Correlation Matrix (ACM) across all seen classes, where the intra-task relationships derive from the hard label statistics. In contrast, the inter-task relationships leverage hard and soft labels from data and a constructed expert network. Then, we propose a novel partial label encoder (PLE) for MLCL, which can extract dynamic class representation for each partial label image as graph nodes and help generate soft labels to create a more convincing ACM and suppress forgetting. Last, to suppress the forgetting of label dependencies across old tasks, we propose a relationship-preserving constrainter to construct label relationships. The inter-class topology can be augmented automatically, which also yields effective class representations. The proposed method is evaluated using two multi-label image benchmarks. The experimental results show that the proposed way is effective for MLCL image recognition and can build convincing correlations across tasks even if the labels of previous tasks are missing.