Graph　Neural　Networks　(GNNs)　have　shown　great　performance　in　learning　representations　for　graph-structured　data.　However,　recent　studies　have　found　that　the　interference　between　topology　and　attribute　can　lead　to　distorted　node　representations.　Most　GNNs　are　designed　based　on　homophily　assumptions,　thus　they　cannot　be　applied　to　graphs　with　heterophily.　This　research　critically　analyzes　the　propagation　principles　of　various　GNNs　and　the　corresponding　challenges　from　an　optimization　perspective.　A　novel　GNN　called　Graph　Neural　Networks　with　Soft　Association　between　Topology　and　Attribute　(GNN-SATA)　is　proposed.　Different　embeddings　are　utilized　to　gain　insights　into　attributes　and　structures　while　establishing　their　interconnections　through　soft　association.　Further　as　integral　components　of　the　soft　association,　a　Graph　Pruning　Module　(GPM)　and　Graph　Augmentation　Module　(GAM)　are　developed.　These　modules　dynamically　remove　or　add　edges　to　the　adjacency　relationships　to　make　the　model　better　fit　with　graphs　with　homophily　or　heterophily.　Experimental　results　on　homophilic　and　heterophilic　graph　datasets　convincingly　demonstrate　that　the　proposed　GNN-SATA　effectively　captures　more　accurate　adjacency　relationships　and　outperforms　state-of-the-art　approaches.　Especially　on　the　heterophilic　graph　dataset　Squirrel,　GNN-SATA　achieves　a　2.81%　improvement　in　accuracy,　utilizing　merely　27.19%　of　the　original　number　of　adjacency　relationships.　Our　code　is　released　at　https://github.com/wwwfadecom/GNN-SATA.