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# Graph to Graph: a Topology Aware Approach for Graph Structures Learning and Generation

*Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics*, PMLR 89:2946-2955, 2019.

#### Abstract

This paper is concerned with the problem of learning the mapping from one graph to another graph. Primarily, we focus on the issue of how to effectively learn the topology of the source graph and then decode it to form the topology of the target graph. We embed the topology of the graph into the states of nodes by exerting a topology constraint, which results in our Topology-Flow encoder. To decoder the encoded topology, we design a conditioned graph generation model with two edge generation options, which result in the Edge-Bernoulli decoder and the Edge-Connect decoder. Experimental results on the 10-nodes simple graph dataset illustrate the substantial progress of the proposed method. The MNIST digits skeleton mapping experiment also reveals the ability of our approach to discover different typologies.