laplacian positional encoding
aristo-panhu opened this issue · comments
how to deal with the laplacian positional encoding of directed graph? The adjacency matrix of a directed graph is not an identity matrix.
Hi @aristo-panhu,
can you please clarify a little on the query? Usually, eigenvectors of (other) matrix of the graph structure (Laplacian is an eg.) can be used as well to compute PEs.
I use your method to encode Directed Acyclic Graph(DAG), which adjacency matrix is a nilpotent matrix(which is a upper triangular matrix and its diagonal element is 0). I use your method to calculate its Laplace eigenvector. I find that its eigenvalues all are 1, and only the first value of all eigenvectors is non-0. Therefore, such eigenvector cannot contain the structure information of the graph. How to deal with this situation?