The recognition of operational state patterns is crucial for the safe, reliable and profitable operational management of integrated energy systems (IES). However, considering that the monitored operational data are often not labelled, supervised machine learning classification methods cannot be directly applied. In this study, based on the idea of graph theory, a framework of interpretable time series pattern recognition methods based on graph structural features is proposed. Firstly, the time series data is segmented into local subsequences by a shapelet-based time series classification method. Secondly, time-graphlets are constructed by means of a visibility graph algorithm and an original graph structure feature-based representation method is proposed. Then, pattern recognition of the different operational states of IES is performed in the form of multidimensional feature vectors. Thirdly, an association rule model is designed to analyze the supply and demand fluctuations, price fluctuations and couplings between multiple energy subsystems, based on which the pattern recognition results are annotated to match the operational characteristics of the IES. Fourthly, a shapelet-based state transfer network graph is constructed, and the complex network centrality metrics are used to analyze the operating characteristics and key operating states of the system over time. The new method is applied for pattern recognition of operational states in a Spanish IES. The results show that the proposed method can increase the interpretability of the recognition results and provide explanatory labels for the operational data. Furthermore, the vulnerable operational states of the system can be revealed, which allows managers to monitor the operational state of the system and take early defensive measures against the more threatening operational patterns. This suggests that the methodological framework presented in this paper is a promising approach to pattern recognition that can provide interpretable annotations for unsupervised operational data of IES and their safe management.