A quantitative understanding of dynamic lane-changing interaction patterns is indispensable for improving the decision-making of autonomous vehicles (AVs), especially in mixed traffic with human-driven vehicles. This paper develops a novel framework combining the hidden Markov model (HMM) and graph structure to identify the difference in dynamic interaction patterns between mandatory lane changes (MLC) and discretionary lane changes (DLC). An HMM is developed to separate the interaction patterns considering heterogeneity in lane-changing processes and reveal the temporal properties of these patterns. Conditional mutual information is used to quantify the interaction intensity, and the graph structure is used to characterize the relationship between vehicles. Finally, a case study is conducted to demonstrate the practical value of the proposed framework and validate its effectiveness in predicting lane-changing trajectories. Based on the lane-changing events extracted from a real-world trajectory dataset, the proposed analytical framework is applied to model MLC and DLC under congested traffic with levels of service E and F. The results show that there could be multiple heterogeneous dynamic interaction patterns in a lane-changing process. A comparison of MLC and DLC demonstrates that MLC involves more intense interactions and more frequent transitions of the interaction network structure, while the evolution rules of interaction patterns in DLC do not exhibit a clear trend. The findings in this study are useful for understanding the connectivity structure between vehicles in lane-changing interactions and for designing safe and smooth driving decision-making models for AVs and advanced driver-assistance systems.