The intro pic shows the pencil on a key chain.
Step 1: How it Works
Step 2: Materials And Mixing
Gorilla Glue or Elmers white glue
Carbon Graphite available as lubricating graphite from a hardware store.
100% silicone caulk
Plastic mixing cup and mixing stick
Mix 3 measures of Carbon Graphite by volume with enough water to form a thick paste. Add 2 measures of white glue and mix well. Spoon the mix onto some polyethylene plastic on a flat surface. Spread it out 3/16" to 1/4" thick at a diameter large enough for the pencil.
Unfortunately I have not found a way to get it to set up faster, so it usually takes 3 or 4 days to totally harden up. While drying, it will shrink and warp a bit.
Because it has so much carbon which strengthens the plastic, it also works quite well as a pencil lead. It is hard enough to not rub off on your hands but soft enough to make smear less lines on paper that are light but very readable.