Most airlines will allow 13 year olds to fly alone but their policies can vary so it's best to check with the airline that the 13 year old will be flying alone on to get exact details.
But here's a list of Airlines I know about that will allow a 13 year old to fly alone.
Alaska Airlines, American Airlines, British Airways, Delta Air Lines, Frontier Airlines, Hawaiian Airlines, Icelandair and Canada Air.
Those are all Airlines that allow 13 year olds to fly solo.