Which of the following sentences are correct?
The relation between any two nodes is associated with a real number that indicates the probability.
The relation between two arbitrary nodes is associated with a real number that indicates the probability.
The relation between two nodes is associated with a real number that indicates the probability.
While the sentences are grammatically correct, they are backwards in that they emphasize association of two nodes with a number. That may be what you mean; but more probably, the sentences should say a number is associated with any pair of nodes. For example:
Each pair of nodes has a probability assigned to it.
If you need to emphasize that a real-number datatype is used for representing probability values, add real-number before probability in the above; otherwise, leave it out, as it's just clutter.
As @SrJoven has commented, they're all "correct" grammatically.
So the question is, which is correct for your intended meaning?
If the first sentence (any) conveys your intended meaning correctly, then the latter two are inferior. This is because they both imply qualification in some way of which nodes this can be said about. (Either they must be arbitrary nodes, whatever that could mean in a given context, or in the other case, the statement might be true about two particular nodes and not other nodes.)
