The alarm was reported to have been raised after a suspicious object was detected in the screening area.
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However, it was later found to have been a false alarm, with passengers then being allowed to return.
Travellers have been urged to check their flight information after some flights were diverted and others delayed.
A spokesman for Police Scotland said: “Operations at the airport have now returned to normal and those within the building are thanked for their patience and co-operation.
“Police Scotland can now confirm that the object found at Edinburgh Airport has now been inspected and is of no danger to the public.”
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