I just read this story on MIT working on industrial scale, km^2 sheet production of graphene.
A quick check of Wikipedia on graphene and Wikipedia on space elevator tells me
Measurements have shown that graphene has a breaking strength 200 times greater than steel, with a tensile strength of 130 GPa (19,000,000 psi)
and
The largest holdup to Edwards' proposed design is the technological limit of the tether material. His calculations call for a fiber composed of epoxy-bonded carbon nanotubes with a minimal tensile strength of 130 GPa (19 million psi) (including a safety factor of 2)
Does this mean we may soon actually have the material for a space elevator?
Answer
A decent terrestrial space elevator could be built with a material with a tensile strength of 50 Gigapascals (including a decent safety factor), so this material may suffice.
Note that there is no prospect of having one 100,000 km nanotube - they would actually be much shorter (maybe 10 cm) and held together by the much weaker inter-tube molecular bonds (if the strings are long enough, they will bond together billions of times where they touch; if there are enough such contact points, the inter-tube bond can be as strong as you want.
Graphene uses the same carbon-carbon bond as the nanotubes for strength, so it would not surprise me if graphene could be used to create strong tethers. I think that what is really holding the terrestrial space elevator back is the lack of money for elevator-focused R&D on string materials. There is really no other market for these materials, and other uses (such as bullet-proof vests) are not close enough to
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