NL – iterating all edges of a graph in log space

Given a turing machine which has logrtmic space, and consists of an input tape and a working tape, Is it possible to iterate all egdes of an input graph? I know the answer is probably NO, because clique and other similer NP problems belongs to NP and not to NL. Unfortunately, I can’t find a satisfying and clear explanation to that fact. Can some one make it more clear for me?