Planar graph

A graph that can be drawn with no edges overlapping.

Graphs may be already drawn with edges overlapping. If they can be “untangled” in a way where no edges overlap, then it is planar. Hence, the emphasis on “can”.

Example

Faces

When a planar graph is drawn with no edges overlapping, a face is a bounded area between edges.

In the example above, the planar graph would have 3 faces, as everything outside the graph is considered a face.

Eulers formula

Euler’s formula states that:

$$v+f=e+2$$

where $v$ denotes the number of vertices, $f$ denotes the number of faces, $e$ denotes the number of edges.