We propose analysis of multiple spin states in radical carbon zigzag edge graphene-like molecules. Calculations based on density function theory (DFT) revealed that the highest spin state was most stable in every radical carbon edge asymmetric molecule. A typical C₆₄H₁₇ molecule has five unpaired electrons, which creates three possible molecular spin states of Sz=1/2, 3/2, and 5/2. The Sz=5/2 state was the most stable among these states. Such DFT results coincided with a simple magnetic counting rule to give a localized spin of Sz=+2/2 to one radical carbon site, whereas it gave Sz=-1/2 at the nearest carbon and +1/2 at the second nearest. A total molecular spin of Sz was obtained by using the simple sum of those numbers. Radical carbon zigzag edge nano-graphene is a promising candidate for designing new materials with strong magnetism. In addition, we studied oxygen-substituted zigzag edges occupied by four electrons. These four spins canceled each other out in two tetrahedral orbits, which led to weak molecular magnetism.