Tensor invariants can be viewed as sums over the proper edge colorings of certain planar bipartite graphs called SL_r webs. In this talk, I will introduce SL_r webs and discuss ongoing work studying the structure of the set of edge colorings of an SL_r web. An (edge) Kempe move on an edge coloring of a graph swaps two colors along a maximal path in the graph that uses only those two colors. We can use these moves to construct a graph P(W,r) whose vertices are r-edge colorings of an SL_r web W and whose edges correspond to Kempe moves. I will show that P(W,r) is connected and that it is a poset! I present a few questions about the structure of this poset and answer some of them.