Title: On the Expressive Equivalence Between Graph Convolution and Attention Models. Abstract: Graph neural networks (GNNs) have achieved remarkable successes in various graph tasks, and recent years have witnessed a flourishing growth in research regarding GNNs' expressive power. The number of linear regions generated from GNNs is a recently considered metric that quantifies GNNs' capacity. The estimate of the number of linear regions has been previously developed for deep and convolution neural networks (DNN and CNN). In this paper, we compare the expressive power of the classic graph convolution network (GCN) and attention based models in terms of their capability to generate linear regions. We show that the prediction advantage of attention models can be matched or even surpassed by enhancing GCN with refined graph Ricci curvature resulting the so-called high rank graph convolution network (HRGCN). Thus, the two models are equivalent to each other in terms of expressive power. Experimental results show that the proposed HRGCN model outperforms the state-of-the-art results in various classification and prediction tasks.