Hi,
It's the preposition needed after edge (when edge means advantage): edge + over + somebody.
Cambrigde Dictionary:
edge: an advantage over other people
In terms of experience, she definitely had the edge over the other people that we interviewed.
edge (singular, uncountable)
something that gives you an advantage over others: Companies are employing more research teams to get an edge.
The next version of the software will have the edge over its competitors.
edge (on / over sb/sth) a slight advantage over sb/sth:
The company needs to improve its competitive edge.
They have the edge on us.