Papers › Simple Path Structural Encoding for Graph Transformers
Simple Path Structural Encoding for Graph Transformers
Louis Airale, Antonio Longa, Mattia Rigon, Andrea Passerini, Roberto Passerone
Graph transformers extend global self-attention to graph-structured data, achieving notable success in graph learning. Recently, random walk structural encoding (RWSE) has been found to further enhance their predictive power by encoding both structural and positional information into the edge representation. However, RWSE cannot always distinguish between edges that belong to different local graph patterns, which reduces its ability to capture the full structural complexity of graphs. This work introduces Simple Path Structural Encoding (SPSE), a novel method that utilizes simple path counts for edge encoding. We show theoretically and experimentally that SPSE overcomes the limitations of RWSE, providing a richer representation of graph structures, particularly for capturing local cyclic patterns. To make SPSE computationally tractable, we propose an efficient approximate algorithm for simple path counting. SPSE demonstrates significant performance improvements over RWSE on various benchmarks, including molecular and long-range graph datasets, achieving statistically significant gains in discriminative tasks. These results pose SPSE as a powerful edge encoding alternative for enhancing the expressivity of graph transformers.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections