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We analyzed the adsorption of Li on graphene in the context of anodes for lithium-ion batteries (LIBs) using first-principles methods including van der Waals interactions. We found that although Li can reside on the surface of defect-free graphene under favorable conditions, the binding is much weaker than to graphite and the concentration on a graphene surface is not higher than in graphite. At low concentration, Li ions spread out on graphene because of Coulomb repulsion. With increased Li content, we found that small Li clusters can be formed on graphene. Although this result suggests that graphene nanosheets can conceivably have a higher ultimate Li capacity than graphite, it should be noted that such nanoclusters can potentially nucleate Li dendrites, leading to failure. The implications for nanostructured carbon anodes in batteries are discussed.