Edge-Girth as a Structural Edge Feature for Graph Neural Networks
Graph neural networks (GNN) based on message passing are provably no more powerful than the one-dimensional Weisfeiler--Leman colour-refinement test (1-WL): two graphs it cannot tell apart receive identical representations, however deep or wide the network. A common remedy augments node or edge features with precomputed structural descriptors, most often counts of a fixed small subgraph such as triangles or longer cycles, but such counts require committing in advance to the size of the substructure counted, a choice usually made blind to the data. We study a descriptor that avoids this choice. The edge-girth of an edge is the length of a shortest cycle through it, and its multiplicity is ...
| Authors | Lilian Marey, Charlotte Laclau |
|---|---|
| Primary category | cs.LG |
| Published | 1 September 2026 |
| Last updated at source | 1 September 2026 |
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