TECHNOLOGY FOCUS - POLYMERS - Preferred Parameter: The chemical bond is a covalent bond or an ionic bond. An average thickness of the graphene films is 100 nm or less. The graphene films are porous. Preferred Components: The covalent bond includes at least one selected from an ester group, an ether group, a carbonyl group, an amide group, a carbonate anhydride group, and an acid anhydride group; or the ionic bond includes at least one selected from a carboxylic acid ion, an ammonium ion, and an acyl cation group. Each of the graphene films comprises electrolyte-permeable pores. The nanomaterial is shaped in the form of a particle, a tube, a wire, a rod, a fiber, an arbitrary bulk, or its combined shape. It is at least one selected from a carbon-based nanomaterial, a metal-based nanomaterial, a metal compound-based nanomaterial, a polymer-based nanomaterial, and its combination. The carbon-based nanomaterial includes at least one selected from carbon nanotubes, carbon nanoparticles, carbon nanowires, carbon nanofibers, fullerene, graphite, activated carbon, soft carbon including carbon calcined at a low temperature, hard carbon including carbon calcined at a high temperature, pitch carbide, mesophase pitch carbide, and calcined cokes. The metal-based nanomaterial includes at least one selected from lithium, sodium, potassium, rubidium, cesium, iridium, nickel, manganese, vanadium, titanium, chromium, silver, molybdenum, tungsten, gold, iron, lead, tin, copper, strontium, zirconium, magnesium, barium, alloy and its mixture. The metal compound-based nanomaterial includes at least one selected from a metal oxide, a metal nitride, a metal sulfide, a metal carbide, and a metal halide. The polymer-based nanomaterial includes at least one selected from polystyrene, polyimide, polyamide, polyvinyl pyrrolidone, polyvinyl, polyvinyl alcohol, polyethyleneoxide, polyurethane, polymethyl mathacrylate, and polypropylene. Preferred Composition: A density of the graphene-nanomaterial composite is in a range of 0.1 g/cm3 (cc) to 10.0 g/cc. EXAMPLE - No suitable example given.