A planar graph is a collection of nodes and edges in 2D space.
letplanarGraph = newPlanarGraph()
The simple application of a 2D position to every node ushers in a new set of rules and ways of orienting oneself to the graph.
Positions are mapped to the Euclidean plane and are described in terms of X and Y. Two adjacent edges create an interior angle between them. It's now possible for nodes and edges to be near in proximity to each other. Edges can enclose a space to create a face.
It's now possible for edges to cross each other, something traditionally not allowed in mathematics. Two crossing edges should be resolved into four edges with a new node sitting at their intersection.