Editing Planar graph (section)

=== Average degree ===

Connected planar graphs with more than one edge obey the inequality {{math|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 {{math|1=''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.