Friday, February 15, 2013

what's the name of that graph

The Edge, with its deep thoughts and long interviews, seems at odds with typical Internet culture, and yet is representative of a particular type of discourse that could only exist with the Internet - or maybe the conversations like those at the Edge would exist without the net, but most of us would have no access to them.

Content aside, I noticed the graphic above in the promotional material for the new Edge book, This Explains Everything. At first I thought it was a complete graph on 12 vertices (K_12) - which you would think make a nice choice of graphic to represent the fully networked world that the Edge folk themselves exemplify (it has all possible edges).

But if you look again at the image on the graphic (sorry it is small), you'll see that this isn't quite right. It really looks more like this:

This graph is, I think, the sum of the complete graph on eight vertices and the empty graph on four vertices. The sum of two graphs is formed by taking both graphs and connecting the vertices from one graph to all the vertices of the other.