structural:expansion, information:highlighting
Average degree

Connected planar graphs with more than one edge obey the inequality 2 e ≥ 3 f, because each face has at least three face-edge incidences and each edge contributes exactly two incidences. It follows via algebraic transformations of this inequality with Euler's formula v – e + f = 2 that for finite planar graphs the average degree is strictly less than 6. Graphs with higher average degree cannot be planar.