A learned triangle-selection module rewires graphs for GNNs, improving node classification over prior rewiring methods on 9 of 10 benchmarks.
Diameter and spectral gap for planar graphs
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abstract
We prove that the spectral gap of a finite planar graph $X$ is bounded by $\lambda_1(X)\le C(\frac{\log(\diam X)}{\diam X})^2$ where $C$ depends only on the degree of $X$. We then give a sequence of such graphs showing the the above estimate cannot be improved. This yields a negative answer to a question of Benjamini and Curien on the mixing times of the simple random walk on planar graphs.
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Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networks
A learned triangle-selection module rewires graphs for GNNs, improving node classification over prior rewiring methods on 9 of 10 benchmarks.