Identifying the essential characteristics and forecasting carbon prices is significant in promoting green transformation. This study transforms the time series into networks based on China's pilots by using the visibility graph, mining more information on the structure features. Then, we calculate nodes' similarity to forecast the carbon prices by link prediction. To improve the predicted accuracy, we notice the node distance to introduce the weight coefficient, measuring the impact of

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... nodes on future nodes. Finally, this study divides eight pilots into different communities by hierarchical clustering to study the similarities between these pilots. The results show that eight pilots are the "small world" networks except for Chongqing and Shenzhen pilots, all of which are "scale-free" networks except for Shanghai and Tianjin pilots. Compared with other predicted methods, the proposed method in this study has good predicted performance. Moreover, these eight pilots are divided into three clusters, indicating a higher similarity in their price-setting schemes in the same community. Based on the analysis of China's pilots, this study provides references for carbon trading and related enterprises.