Graph Embeddings

Laplacian Positional Encodings

Introduced by Dwivedi et al. in Benchmarking Graph Neural Networks

Laplacian eigenvectors represent a natural generalization of the Transformer positional encodings (PE) for graphs as the eigenvectors of a discrete line (NLP graph) are the cosine and sinusoidal functions. They help encode distance-aware information (i.e., nearby nodes have similar positional features and farther nodes have dissimilar positional features).

Hence, Laplacian Positional Encoding (PE) is a general method to encode node positions in a graph. For each node, its Laplacian PE is the k smallest non-trivial eigenvectors.

Source: Benchmarking Graph Neural Networks


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Component Type
Graph Embeddings