6,257 research outputs found
Gradual Weisfeiler-Leman: Slow and Steady Wins the Race
The classical Weisfeiler-Leman algorithm aka color refinement is fundamental
for graph learning and central for successful graph kernels and graph neural
networks. Originally developed for graph isomorphism testing, the algorithm
iteratively refines vertex colors. On many datasets, the stable coloring is
reached after a few iterations and the optimal number of iterations for machine
learning tasks is typically even lower. This suggests that the colors diverge
too fast, defining a similarity that is too coarse. We generalize the concept
of color refinement and propose a framework for gradual neighborhood
refinement, which allows a slower convergence to the stable coloring and thus
provides a more fine-grained refinement hierarchy and vertex similarity. We
assign new colors by clustering vertex neighborhoods, replacing the original
injective color assignment function. Our approach is used to derive new
variants of existing graph kernels and to approximate the graph edit distance
via optimal assignments regarding vertex similarity. We show that in both
tasks, our method outperforms the original color refinement with only moderate
increase in running time advancing the state of the art
Generation of cubic graphs
We describe a new algorithm for the efficient generation of all non-isomorphic connected cubic graphs. Our implementation of this algorithm is more than 4 times faster than previous generators. The generation can also be efficiently restricted to cubic graphs with girth at least 4 or 5
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