not graphite- that's in pencils. granite, like fancy rockwork and countertops. if you're wondering if it's inert, soak it in a bucket of water for a few weeks and check the parameters of the water as you go. probably distilled water would be best, so it has a low KH and GH
By the green tone it looks like it has chlorite in it. It depends if the green is from plant or staining or if its the color of the minerals in it. If it is grey after rinsing it off with some cloudy grey crystals than this is most likely has quartz and the rock would be a granite. Granite vary in composition, they most contain quartz but there could be plagioclase, orthoclase, biotite and many other minerals in it.