A scalable method for mining graph patterns stable under subsampling is proposed. The existing subsample stability and robustness measures are not antimonotonic according to definitions known so far. We study a broader notion of anti-monotonicity for graph patterns, so that measures of subsample stability become antimonotonic. Then we propose gSOFIA for mining the most subsample-stable graph patterns. The experiments on numerous graph datasets show that gSOFIA is very efficient for discovering subsample-stable graph patterns.