That's right, but we don't need to use the Euclidean distance directly, and in fact most often we don't. For example, we usually use dot product, and predict su

That's right, but we don't need to use the Euclidean distance directly, and in fact most often we don't. For example, we usually use dot product, and predict success between two users as sigmoid(A.B), then we can have A.B > 0 and B.C > 0 but A.C < 0, so there's no problem. We can get the same with Euclidean metric too, by (soft) thresholding- anyway we have to map from our distance to a prediction of the interaction somehow.