Comparison of Biological Graph Alignment Algorithms With Hyperbolic Heterophilic Deep Graph Learning-Based Approach

Network alignment is a fundamental task in biological network analysis, aiming to identify corresponding nodes across multiple graphs such as protein–protein interaction (PPI) networks. Existing alignment methods struggle to capture the heterophily, hierarchical organization, and higher-order structures commonly observed in real biological networks. To address these challenges, we propose HMGA (Hyperbolic Graph Learning for Multi-Perspective Graph Alignment), a unified framework that integrates hyperbolic and Euclidean representation learning within hypergraph modeling to take into account higher-order structures. It also utilizes a heterophily-aware graph attention network to model heterophily and heterogeneity. HMGA simultaneously encodes first-order, power-law, and higher-order topological features by leveraging hyperbolic geometry to mitigate embedding distortion in scale-free structures while maintaining Euclidean consistency for regular subgraphs. The model fuses multiple alignment matrices generated from distinct embedding spaces to achieve robust cross-network correspondence. To discuss the advantages of the proposed approach, we bring together a fair evaluation framework that systematically compares the performance of different network alignment approaches. Experiments on both synthetic and real-world biological datasets, including Human–Yeast, C. jejuni–E. coli, and A. thaliana–D. melanogaster PPIs, demonstrate that HMGA performs reasonably with respect to state-of-the-art baselines in TOP-K accuracy. Furthermore, HMGA successfully identifies known and novel functional orthologs across distant eukaryotes, validating its biological relevance. Even though many graph alignment methods have been proposed recently, there is no recent systematic comparison of all these methods, which is another contribution of this study.