# Graph Structure and Isomorphism Learning: A Survey

### Abstract

With the great success of artificial intelligence in recent years, graph learning is gaining attention from both academia and industry [1, 2]. The power of graph data is its capacity to represent numerous complicated structures in a broad spectrum of application domains including protein networks, social networks, food webs, molecular structures, knowledge graphs, sentence dependency trees, and scene graphs of images. However, designing an effective graph learning architecture on arbitrary graphs is still an on-going research topic because of two challenges of learning complex topological structures of graphs and their nature of isomorphism. In this work, we aim to summarize and discuss the latest methods in graph learning, with special attention to two aspects of structure learning and permutation invariance learning. The survey starts by reviewing basic concepts on graph theory and graph signal processing. Next, we provide systematic categorization of graph learning methods to address two aspects above respectively. Finally, we conclude our paper with discussions and open issues in research and practice.

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