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Aiming at the problem of mining the features of topology nodes deficiently in the existing inexact graph matching, this paper proposes an improved graph convolutional network (GCN) model for inexact graph matching. Firstly, considering that the selecting nodes should have strong representation, three methods of measuring the centrality of network nodes in the social network analysis are used to obtain the centrality of nodes of graph, and the nodes are sorted based on the size of node centrality. Secondly, for the nodes and edges of graph have corresponding domain features, when mapping the topology to the grid structure, the relationship attributes between the nodes should be maximized. When the node neighborhood size does not meet the receptive field threshold, the centrality is sorted and the neighborhood nodes are sequentially acquired according to the centrality until the neighborhood size meets the receptive field threshold. Then the convolutional neural network is used to classify and identify the graph. Finally, training and testing are performed on multiple standard graph datasets. The experimental results show that the improved GCN model has higher recognition rate than other similar methods in graph matching.