The graph convolutional layer is core in the architecture of graph convolutional neural networks (CNNs). In the literature, both spectrum domain based and vertex domain based graph convolutional layers have been proposed. This paper analyzes these two types of graph convolutional layers and demonstrates that the spectrum domain based graph convo-lutional layer suffers from output inconsistencies when the graph shift matrix has repeated eigenvalues. In contrast, the vertex domain based graph convolutional layer is output consistent and inherits the local feature extraction property of classical CNNs with low computational complexity. Experimental results on different data sets also demonstrate that vertex domain based graph CNNs exhibit better performance than existing methods for classification problems.