Plot a planar graph as a planar graph?

I've got an application dealing with planar graphs where the fact that they're planar is important, and so my representations of those graphs should emphasise this. However, when I use plot() to plot them, it often creates unnecessary overlapping edges. None of the 'Layout' options correspond to planarity, and none of them seem to prevent the problem in all cases.

Is there a way, given an arbitrary planar graph, to have Matlab plot it while respecting that planarity? I do not want to generate points to place the nodes; I would like Matlab to do that automatically.