Title: Graph Deformer Network. Abstract: Convolution learning on graphs draws increasing attention recently due to its potential applications to a large amount of irregular data. Most graph convolution methods leverage the plain summation/average aggregation to avoid the discrepancy of responses from isomorphic graphs. However, such an extreme collapsing way would result in a structural loss and signal entanglement of nodes, which further cause the degradation of the learning ability. In this paper, we propose a simple yet effective graph deformer network (GDN) to fulfill anisotropic convolution filtering on graphs,  analogous to the standard convolution operation on images. Local neighborhood subgraphs (acting like receptive fields) with different structures are deformed into a unified virtual space, coordinated by several anchor nodes. In space deformation, we transfer components of nodes therein into anchors by learning their correlation, and build a pseudo multi-granularity plane calibrated with anchors. Anisotropic convolutional kernels can be further performed over the anchor-coordinated space to well encode local variations of receptive fields. By parameterizing anchors and stacking coarsening layers, we build a graph deformer network in an end-to-end fashion. Theoretical analysis indicates its connection to previous work and shows the promising property of isomorphism testing. Extensive experiments on widely-used datasets validate the effectiveness of the proposed GDN in node and graph classifications.