Constructing self-complementary graphs How does one go about systematically constructing a self-complementary graph, on say 8 vertices?
[Added: Maybe everyone else knows this already, but I had to look up my guess to be sure it was correct: a self-complementary graph is a simple graph which is isomorphic to its complement.  --PLC]

If you have a self-complementary graph of order 4n, half the vertices must each lie on fewer than 2n edges and the other half must lie on 2n or more edges. Add a vertex by connecting it to the 2n vertices lying on fewer than 2n edges. The result is a self-complementary graph of order 4n+1.
You can create a second self-complementary graph of order 4n+1 by taking the self-complementary graph of order 4n and connecting the new point to the 2n vertices lying on 2n or more edges. 
