HopGAT: A multi-hop graph attention network with heterophily and degree awareness

In highly heterophilic graphs, where nodes frequently connect across categories, the attention learning mechanism by dynamically adjusting neighboring node weights, may struggle to capture intricate node relationships. Furthermore, first-hop neighbor information is usually insufficient to encompass the global structure, but multi-hop increases complexity. To address these challenges, we propose HopGAT, a multi-hop graph attention network with heterophily and degree awareness. Firstly, we design heterophily-based neighbor sampling to sequentially filter high-hop neighbors by degree. Next, to obtain comprehensive global information, we construct a multi-hop recursive learning method with head and tail attention vectors to learn multi-hop neighbor features. Finally, we combine the average node degree of the graph with hop decay modeling to learn importance coefficients at different hops and adaptively aggregate the learned multi-hop features. Experimental results demonstrate that HopGAT significantly improves performance across 9 benchmark datasets with various heterophily and different average degrees.