Graphite electrode is nothing more than a sharp graphite rod, taken from a pile, subject to a support conductor of the current, copper tube, and at a reasonable distance a plastic handle, PVC tube. The handle should be far enough away so that it does not reach so much heat to soften it. Anyway it is clear that PVC is the worst plastic that can be used for this but it was there.
This is a sheet metal welder for almost any metal. It does not require input of material and practically does not admit it unless they are very thin rods. It is not about electric arc welding. What melts the metal is the graphite tip that shortly turns to bright white. What is heated by the current is graphite, not metal, Graphite electrode because the first one has a much greater resistance and dissipates most of the power. It is important that the graphite tip is sharp for two reasons:
The finer the point of contact between the material and the tip more resistance to current and more temperature reach. If it is too thick, heat is transmitted easily from the tip to the soldering iron and a large part of it dissipates without reaching the necessary temperature. The soldering iron only works if it concentrates most of the power at the point to be soldered. Everything has to be thought for that.