We have studied magnetization of graphene nanocrystals obtained by sonic exfoliation of graphite. No ferromagnetism is detected at any temperature down to 2~K. Neither do we find strong paramagnetism expected due to the massive amount of edge defects. Rather, graphene is strongly diamagnetic, similar to graphite. Our nanocrystals exhibit only a weak paramagnetic contribution noticeable below 50~K. The measurements yield a single species of defects responsible for the paramagnetism, with approximately one magnetic moment per typical graphene crystallite.