When working from a graph in flat even count peyote stitch, you will not have to do any extra stitching to position yourself for beginning each row.
Every other row will end with either an “inside” bead or an “outside” bead. The outside beads are on the very edge of the piece. The inside beads are directly next to the outside beads on the interior of the piece.
Because the sides are slightly offset from one another, this will make it a little easier to find your place if you lose track while you are working.