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It has do to with a phenomenon known as electron delocalisation. Graphite is the only form of carbon (and one of the only non-metals) to conduct electricity. Graphite is arranged in sheets of 6-membered rings, and these sheets have delocalised electrons, which means that electrons are spread evenly throughout the sheet and are free to move, and therefore carry electrical charge throughout the sheet.

Other forms of carbon, such as diamond, do not have delocalised electrons, and are insulators.

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