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With the development of the Internet, multimedia data grows by an exponential level. The demand for video organization, summarization and retrieval has been increasing where scene detection plays an essential role. Existing shot clustering algorithms for scene detection usually treat temporal shot sequence as unconstrained data. The graph based scene detection methods can locate the scene boundaries by taking the temporal relation among shots into account, while most of them only rely on low-level features to determine whether the connected shot pairs are similar or not. The optimized algorithms considering temporal sequence of shots or combining multi-modal features will bring parameter trouble and computational burden. In this paper, we propose a novel temporal clustering method based on graph convolution network and the link transitivity of shot nodes, without involving complicated steps and prior parameter setting such as the number of clusters. In particular, the graph convolution network is used to predict the link possibility of node pairs that are close in temporal sequence. The shots are then clustered into scene segments by merging all possible links. Experimental results on BBC and OVSD datasets show that our approach is more robust and effective than the comparison methods in terms of F1-score.