A graph is called planar if it can be drawn in the plane without any intersecting edges. The number of planar graphs with 1, 2, 3, ... vertices is 1, 2, 7, 34, 257, 2606, ... . Use the sliders to generate all the planar graphs with nine or fewer vertices. They are randomly projected into the plane, with any overlapping vertices or intersecting edges colored red. Drag the vertices to get rid of the overlaps and intersections!