In this YouTube video, a fellow runs 10 amps through a cylinder of pencil graphite, burning his fingers (accidentally on purpose, I’d say).
He has a good article about graphite on his site:
Graphite is highly conductive unlike diamond or wood. But it is conductive along the layers, not perpendicular to them. It has many different applications. Generally it is crushed into powder that can be used to make other components like battery rods, deposited traces on electronics and such.
But pencils are the most basic use of them. If you draw a thick line using pencil on paper and measure the resistance across it, you will see your line is conductive, and if you bring your probes closer on the paper over the line, the resistance gets lower, like a potentiometer.