Validate the random-walk transition rule

Verify whether the random-walk transition rule used by the random-walk endpoint blend permits returns to the starting node, thereby determining the precise behavior of the graph-modified embeddings produced by this transformation.

Background

The random-walk endpoint blend constructs each node representation by averaging the original embeddings of endpoints reached by fixed-length random walks. Whether a walk can return to its starting node affects which embeddings contribute to the modified representation and therefore influences the transformation’s retrieval behavior.

The paper states that returns are possible unless excluded by the transition rule, but indicates that the rule itself has not yet been verified. This leaves the exact behavior of the implemented random-walk transformation unresolved.