In the routine production and operation of nuclear power plants (NPPs), safety management is extremely important, and consequently, a fault detection system yielding high accuracy could provide effective decision support and prevent the accidents to the maximum extent. Most of existing studies are based on the analysis of time-series data, while researches oriented to the implementation of graph data mining are barely seen. In this paper, we propose an improved fault detection method to address this task from the perspective of graph representation learning. By calculating the similarity between indicators, the multivariate temporal sequences of the running characteristics of NPPs have been formulated as a group of graphs with corresponding labels, on which the graph convolutional network (GCN) has been introduced to detect fault samples in the way of graph classification. Compared to conventional supervised learning classifiers, our proposed methodology performs more superior identification of major faults, and the sensitivity regarding significant parameter or settings in the model design has been analyzed to investigate their optimal arrangements. The findings in this article not only present the promising prospects of introducing graph learning techniques into safety management, also indicate that various kinds of digital signals could be reformulated into graph dataset based on which the original task could be executed more effectively in the way of graph representation learning.