Graphite: each carbon forms three strong in-plane sigma bonds in an sp honeycomb layer. The remaining p orbitals form delocalized pi bands, allowing electrical conduction especially along the layers. Much weaker interlayer attraction permits sliding, explaining softness without implying weak in-plane C-C bonds.
Carborundum is silicon carbide, SiC. A suitable structure is a three-dimensional, tetrahedrally coordinated covalent network: each Si has four C neighbors and each C four Si neighbors. Strong directional bonding in all directions resists slip and gives hardness. Its filled bonding states are separated from empty states by a substantial band gap, giving low conductivity when pure and undoped.
“Non-conductor” is the intended contrast with graphite; SiC is more precisely a wide-bandgap semiconductor, whose conductivity can change with doping and temperature.
Potassium intercalates between graphite layers and donates electron density to the graphitic pi system. Occupation of formerly less populated electronic states raises the mobile-carrier density, increasing electrical conductivity under the stated comparison.
The gain is electronic doping of the carbon framework, rather than a claim that potassium strengthens every C-C bond or simply acts as a separate wire through the sample. Intercalation also changes layer separation and scattering, so conductivity depends on both carrier population and mobility.

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