Before you jump down to the comments to chastise us for misspelling graphene, note that graphyne is similar to graphene but not the same. Like graphene, it is a two-dimensional structure of carbon. Unlike graphene, it contains double and triple bonds and does not always form hexagons. Scientists have postulated its existence for decades, but researchers at the University of Colorado Boulder have finally managed to pull it off. You can also download the paper if you want to wade through the details.
Carbon forms like fullerene and graphene are well-known and have many novel uses. Other allotropes of carbon include graphite and diamonds — certainly two things with wildly varying properties. Graphyne has conductivity similar to graphene but may also have other benefits.
The process is called alkyne metathesis, a fancy name for an organic reaction that reforms alkyne bonds. The process does require kinetic and thermodynamic control, including performing the reaction under argon. The entire produced is outlined in the paper under “Methods.” While it takes a little more than a test tube and a bunsen burner, it doesn’t sound like it takes anything too exotic — some chemicals, a Schlenk flask, liquid nitrogen, and a hot oil bath. This is something a well-stocked home lab might be able to pull off.
We still don’t know what to do with the graphene we make, but it isn’t that hard to make it. There are several different methods. Maybe we’ll see DIY graphyne soon.