This paper proposes a new bearing fault diagnosis method which combines sparse wavelet decomposition and graph neural network with sparse connectivity. In our proposed method, the original vibration signal is decomposed into multi-resolution features by the sparse wavelet decomposition based on three typical bearing fault frequency bands in which the bandwidths are determined by the bearing physical parameters and machine rotating speed. The sparse wavelet decomposition generates three sets of sub-bands. The energy values from each sub-band signal set are calculated to form new one-dimensional data representing the energy distribution. Again, each one-dimensional data constitutes a subgraph. Three subgraphs representing the three fault frequency bands, respectively, are sparsely connected through a connection graph. After the sparse connectivity graph is constructed, GraphSAGE is employed instead of the traditional graph convolutional network for deep learning. For the Case Western Reserve University (CWRU) and self-collected bearing datasets, our proposed method can achieve high classification accuracy of 99.73%.