node2vec and out of sample model application

Question

I'm trying to learn how to use node embedding and in particular how to make out of sample predictions.

Let’s assume at time t=0 we have several observations. Each observation has a binomial output 1/0. Observations are linked together in a network. We create embedding using node2vec and we train some kind of model to link the embedding matrix X to the target vector Y (1/0).

Let’s assume at time t=1 we have other observations with no outcome. Observation is linked together in a similar but different network. We create embedding using node2vec always using node2vec with the same parametrization of t=0 and we obtained the X matrix.

Can we apply the model trained in t=0? I suppose that there is not assurance of stability in the embedding matrix X. Am I wrong?

If I am right, is there some kind of different approach that can be used to maintain stable the embedding?

Thx.