In diabetes management, identifying glycemic patterns leading to hypoglycemia, i.e., low blood glucose, plays a key role in preventing, recognizing, and treating hypoglycemic complications and stabilizing the blood glucose levels in the recommended range. The present paper introduces a novel graph-based algorithm for time series clustering and empirically proves its applicability to recognizing risky time intervals leading to hypoglycemia. By means of the novel method, we cluster continuous glucose monitoring records individually for people with Type 1 Diabetes. Eventually, the time information corresponding to the clusters of decreasing trends (leading to hypoglycemia) is incorporated to determine risky time intervals and trends. The experimental results on long-term monitoring records highlight the importance of personalized information. Moreover, the novel method shows promising performance compared with other clustering methods in terms of accuracy and computation time.