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Time complexity for searching an Edge in Graph represented by Adj List

How is the time complexity for searching an Edge in Graph represented by Adj List = O(V)?
According to my understanding it should be O(E). Say I am looking for an edge between vertex A and Vertex B, I go to vertex A in the Adj array list and propagate through all the edges in the linkedlist for that vertex, isn’t this represented by ‘E’?