How did Galadriel knew that Gandalf was back?

[Eöl]

in ROTK : Chapter 6 Many Partings:
concerning Galadriel, Celeborn, Elrond and Gandalf.

Often long after the hobbits were wrapped in sleep they would sit together under the stars, recalling the ages that were gone and all their joys and labours in the world,or holding council, concerning the days to come. If any wanderer had chanced to pass, little would he have seen or heard, and it would have seemed to him only that he saw grey figures, carved in stone, memorials of forgotten things now lost in unpeopled lands. For they did not move or speak with mouth, looking from mind to mind; and only their shining eyes stirred and kindled as their thoughts went to and fro.