You can make graphene at home including your own super capacitors. The real problem here is that it's not stable outside the lab. You hear "tensile strength x steel!", you think OMG this stuff must be the most impressive thing ever.
It's really, really thin flakes of carbon. Take a piece of scotchtape to the shiny side of a piece of coal rub it on smooth and pull it off. Instant graphene! But if you flex it at all it's going to crack. It's not particularly flexible stuff.
Graphene is really strong but only in the nano and micro scale. Researchers are trying to replicate this to the larger scale for applications out of lab.