Graph Positional Encoding

[aditya0by0]

Following encoding from https://arxiv.org/pdf/2003.00982 can be incorporated

Graph Positional Encoding

Nodes in a graph do not have any canonical positional information. In the absence of available features, nodes are anonymous — such as the nodes in the CSL, CYCLES, or GraphTheoryProp datasets in our benchmark. As such, message-passing-based GCNs perform either poorly or fail completely to detect the class of the graph, such as isomorphic classes or cycles (Murphy et al., 2019; Loukas, 2020).

We propose the use of Laplacian eigenvectors (Belkin and Niyogi, 2003) as node positional encodings by building on top of the corresponding dataset files in the data module, as shown in the pseudo-code snippet alongside. In other words, the positional encoding p_i for a node i can be added to its features x_i as:

$$ x_i = x_i + p_i $$

Similarly, other ideas can be explored by leveraging the respective modules of the framework (in Fig. 1), for which we direct the reader to the README of our GitHub repository.