Magically going from a pure topological structure to a 2D straight line embedding. Start with
topo::PlanarGraph G;
// Add a bunch of edges.
G.AddEdge(0, 1); G.AddEdge(1, 2); G.AddEdge(2, 6); G.AddEdge(3, 8);
G.AddEdge(0, 4); G.AddEdge(1, 5); G.AddEdge(2, 7); G.AddEdge(4, 8);
G.AddEdge(0, 5); G.AddEdge(1, 6); G.AddEdge(3, 4); G.AddEdge(4, 9);
G.AddEdge(0, 9); G.AddEdge(2, 3); G.AddEdge(3, 7); ...which according to graphviz's could look like:
Now, we can come up with a function f: V -> R^2 that gives us the following
amazing drawing:
...