Effects of an inversion in the diagram (from ). Observe that the inverted segment is inside the horizontal square bracket, that shows γ2, γ3, ..., γ4, γ5 at the left side and γ5, γ4, ..., γ3, γ2 at the right side of both pictures. (i) If the edges are in the same cycle and with opposite orientations, the inversion splits the cycle. Inversely, if the edges are in different cycles, the inversion joins them (independently of the orientations of the original edges, that are omitted). (ii) If the edges are in the same cycle with the same orientation, the inversion is neutral and the number of cycles remains unchanged.