In this talk, I will introduce plabic graphs and discuss how to classify them using an invariant called trip permutation and a criterion called reduced-ness. In reduced plabic graphs, trip permutations both tell us important information about the postroid cell each plabic graph corresponds to and give us face labels which correspond to clusters in the cluster algebra on positroid varieties. A natural question is: Do non-reduced plabic graphs also have nice combinatorial structures on their trip permutations? I will study a special class of type A non-reduced plabic graphs called "Plabic fences with legs," whose trip permutations have at most 2 disjoint cycles. I will then give a nice way to check if any given cycle arises from the trip permutation of some plabic fence with legs.