A unitary graphene-based integrated heat sink comprising a heat collection member (base) and at least one heat dissipation member (e.g. fins) integral to the baser, wherein the base is configured to be in thermal contact with a heat source, collects heat therefrom, and dissipates heat through the fins. The unitary graphene material is obtained from heat-treating a graphene oxide gel at a temperature higher than 100° C., 500° C., 1,250° C., or 2,000° C., and contains chemically bonded graphene molecules having inter-graphene distance of 0.3354-0.4 nm (preferably mm or cm), exhibiting a degree of graphitization preferably from 1% to 100% and a Mosaic spread value less than 0.7 (preferably no greater than 0.4). The finned heat sink may also be made from a filler-reinforced graphene matrix composite.