Editing Planar graph (section)

===Convex planar graphs===
A planar graph is said to be '''convex''' if all of its faces (including the outer face) are [[convex polygon]]s. Not all planar graphs have a convex embedding (e.g. the complete bipartite graph {{math|K{{sub|2,4}}}}). A sufficient condition that a graph can be drawn convexly is that it is a [[Subdivision (graph theory)|subdivision]] of a [[k-vertex-connected graph|3-vertex-connected]] planar graph. [[Tutte embedding|Tutte's spring theorem]] even states that for simple 3-vertex-connected planar graphs the position of the inner vertices can be chosen to be the average of its neighbors.