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We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sampledoi:10.1103/physrevlett.95.226801 pmid:16384250 fatcat:xh4h4srvdjes5fxv5penvpbaiq