It detects cycles of arbitrary length without preselecting a size.

Graph neural networks, or computer models that process network structures, struggle to tell certain distinct graphs apart. To fix this, researchers usually add counts of small shapes, like triangles. But this forces them to pick the shape sizes ahead of time without knowing the data. The authors studied a different method called edge-girth. For each connection, it finds the length of the shortest loop passing through it and counts how many such shortest loops exist. This captures loops of any size using one simple search per connection. When tested on a molecule dataset called ZINC-12k, their model cut the prediction error to a factor three below the nearest competitor. It matched a method that counts loops up to length eight while using fewer channels. However, if every connection in a graph shares identical loop lengths and counts, the feature becomes uniform, leaving the model unable to separate those graphs.

Why it matters

This helps AI models that predict properties of molecules, like in drug discovery. By avoiding arbitrary choices about which cycle sizes to count, it can make more accurate predictions from graph data.

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