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1.
When a person observes or otherwise hangs around another person IRL (whether it be friend, stranger, or object of misplaced infatuation) without the latter's knowledge. Compare stalking. Phrase originates from the nature shown by Edward Cullen of Twilight, whose obsessive behaviour has been mistaken by millions of young girls as twu lub.

Variants include the past tense 'Edwarded', and 'an Edward' to describe the individual him (or her) self.
"I can hear you breathing around the corner. You fail at Edwarding."

"Damn it, why are you sitting outside my window at 3:00 in the morning?! Stop Edwarding me!"
by _allismine_ August 07, 2009