Title: MeGraph: Graph Representation Learning on Connected Multi-scale Graphs. Abstract: We present MeGraph, a novel network architecture for graph-structured data. Given any input graph, we create multi-scale graphs using graph pooling. Then, we connect them into a mega graph by bridging inter-graph edges according to the graph pooling results. Instead of universally stacking graph convolutions over the mega graph, we apply general graph convolutions over intra-graph edges, while the convolutions over inter-graph edges follow a bidirectional pathway to deliver the information along the hierarchy for one turn. Graph convolution and graph pooling are two core elementary operations of MeGraph. In our implementation, we adopt the graph full network (GFuN) and propose the stridden edge contraction pooling (S-EdgePool) with adjustable pooling ratio, which are extended from conventional graph convolution and edge contraction pooling. The MeGraph model enables information exchange across multi-scale graphs, repeatedly, for deeper understanding of wide-range correlations in graphs. This distinguishes MeGraph from many recent hierarchical graph neural networks like Graph U-Nets. We conduct comprehensive empirical studies on tens of public datasets, in which we observe consistent performance gains comparing to baselines. Specifically, we establish 5 new graph theory benchmark tasks that require long-term inference and deduction to solve, where MeGraph demonstrates dominated performance compared with popular graph neural networks.