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Deep learning for graph matching (GM) has emerged as an important research topic due to its superior performance over traditional methods and insights it provides for solving other combinatorial problems on graph. While recent deep methods for GM extensively investigated effective node/edge feature learning or downstream GM solvers given such learned features, there is little existing work questioning if the fixed connectivity/topology typically constructed using heuristics (e.g., Delaunay ordblp:conf/icml/YuWYL21 fatcat:e442umcg7vgs3muownqyifl5f4