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Tangles are a common anomaly in Automatic Identification System (AIS) data, resulting from disorder in time sequences. They increase the spatial complexity of trajectories, making existing methods unable to fully recognize and process them. This will seriously affect the analysis of ship behavior. Furthermore, existing methods often directly remove after recognition, resulting in a significant loss of local information. To address these challenges, this paper proposes an algorithm called Graph Signal Variation Detection (GSVD) to recognize and reconstruct tangles. Initially, data preprocessing is conducted to remove redundant and stationary points. Then, construct the vertices and edges of the graph using indicators integrating AIS data features and ship trajectories, respectively. The tangled region is identified by calculating the total variation theory of the graph. The tangled region is reconstructed using the greedy heuristic, and the optimal reconstruction path is determined by combining total variation quantization. Finally, the GSVD is compared with four prevailing methods, through qualitative and quantitative analyses. The results demonstrate that the GSVD surpasses the other methods in terms of recognition accuracy, recall rates, and false alarm rates. Additionally, the GSVD can effectively reconstruct the tangle. • Fusion trajectory data features to quantify tangle degree. • A tangled trajectories recognition method based on graph is proposed. • Realizing the reconstruction of tangled trajectories. [ABSTRACT FROM AUTHOR]