  Matrix completion is an important area of research in recommender systems.
Recent methods view a rating matrix as a user-item bi-partite graph with
labeled edges denoting observed ratings and predict the edges between the user
and item nodes by using the graph neural network (GNN). Despite their
effectiveness, they treat each rating type as an independent relation type and
thus cannot sufficiently consider the ordinal nature of the ratings. In this
paper, we explore a new approach to exploit rating ordinality for GNN, which
has not been studied well in the literature. We introduce a new method, called
ROGMC, to leverage Rating Ordinality in GNN-based Matrix Completion. It uses
cumulative preference propagation to directly incorporate rating ordinality in
GNN's message passing, allowing for users' stronger preferences to be more
emphasized based on inherent orders of rating types. This process is
complemented by interest regularization which facilitates preference learning
using the underlying interest information. Our extensive experiments show that
ROGMC consistently outperforms the existing strategies of using rating types
for GNN. We expect that our attempt to explore the feasibility of utilizing
rating ordinality for GNN may stimulate further research in this direction.
