# How to make sense of label propagation formula in graph neural networks?

In the label propagation algorithm in section 3.2.3, we know the label of some nodes and we want to predict the label for the rest of the nodes whose labels we don't know. The update formula for this is the following: $$F(t+1) = \alpha SF(t) + (1-\alpha)Y$$ where $$F(t)$$ is predicted label from timestep t and $$S$$ can be considered as an adjacency matrix, $$Y$$ is the label for both the unlabeled data and labeled data. In the case of labeled data, we initialize $$Y$$ with ground truth and for the unlabeled data, we randomly initialize their label and assign it to $$Y$$. Now, the most problematic part is I think the $$Y$$ matrix. Since I do not know the label of some nodes, so we initialize with some random value and keep Y as a constant throughout this iterative process. We can calculate the optimal value of F directly using: $$F^{*} = (I - \alpha S)^{-1}Y$$ But my question is, if we keep Y as a constant ( assign random numbers to unknown nodes as labels) what kind of sense does it make?