Can someone please explain how at atoms are bonded in Graphite?

Each carbon atom in graphite is connected to 3 other carbon atoms, which are arranged in layers on top of each other. That's why graphite is so smooth and you can write with it. And plus its the only non-metal that can conduct electricity because it's the one carbon is only connected to 3 other carbon atoms, which leaves 1 space free for electricity to conduct.