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Knotting between the beads is important for a variety of reasons. Bead stringing, properly speaking, is a form of rigging. Where a knot is placed, it strengthens the cord three-fold. Consequently, if cord with a tensile strength of 17lbs. The cord is strengthened to 51lbs.10lb-test becomes 30lbs, etc. Thus, it secures the beads. This is especially true when a variety of different sized beads and materials are used. If the cord breaks, there is only one or two beads to pick up off the floor. Losing precious metal beads, or gemstones, can make it costly to repair.
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I use a variety of different stringing material as well. I use anything that will take a knot. Generally, I will use silk, or linen. These are natural fibers, and are quite sturdy and durable. Cotton is too weak. I also use braided kevlar, of varying thicknesses. Kevlar is used in bullet-proof vests, as well as the suits astronauts wear. I often use kevlar with beads that have rough holes.
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I never use tiger-tail,(continued here)
http://annethebeadbear.blogspot.com/2010/05/why-i-knot-between-beads.html