Diamond and graphite are different arrangements of the element carbon, so they are different physically. Graphite is made up of carbon atoms that are covalently bonded to form hexagonal rings.
These hexagonal rings are arranged in layers. There are no strong covalent bonds between each layer. Instead, there are weak intermolecular forces, so the layers can slide over each other. This unique arrangement gives graphite its soft and slippery texture.
Although graphite is made up of a non-metal element, it has similar properties to metals. Graphite has many strong covalent bonds, and it requires a large amount of energy to break them. So, it has a high melting and boiling point.
Each carbon atom in graphite forms three covalent bonds with other carbon atoms, so each carbon atom has a free electron in its outer shell. These electrons are called delocalised electrons. As the delocalised electrons can move, they migrate along the layers. This allows graphite to conduct both electricity and heat.