In industrial systems, fault diagnosis methods playa crucial role for ensuring their safe and stable operations. Among these methods, graph convolutional network (GCN)-based fault diagnosis stands out for its ability to capture complex relationships within data. However, conventional GCN-based methods regard fault diagnosis solely as a classification problem, terminating the diagnostic process once classification decisions are made. This approach overlooks the analysis of the contributions of various relevant variables to the diagnostic results, leading to a lack of explainability and reliability, which hinders their industrial adoption. To address this challenge, the paper proposes a two-stage variables contribution analysis method called graph self- reproductive non-dominated sorting genetic algorithm (Graph-SRGA). The method sequentially conducts neighbor-stage and sensor-stage contribution analysis for the explainability of GCN-based methods. Specifically, two objective functions are formulated as evaluation indicators, and the selection process is encoded into a coding string. The proposed SRGA algorithm, integrating a self-reproductive strategy into the conventional non-dominated sorting genetic algorithm, identifies the required influential set. Experimental validation from various perspectives, using application cases in the high-speed train traction system and the Tennessee Eastman process, demonstrates that the proposed method offers a distinctive solution for the contribution analysis of GCN-based fault diagnosis methods.