Editing Incidence structure (section)

====Levi graph examples ====

The Levi graph of the [[Fano plane]] is the [[Heawood graph]]. Since the Heawood graph is [[Connected graph|connected]] and [[vertex-transitive]], there exists an [[automorphism]] (such as the one defined by a reflection about the vertical axis in the figure of the Heawood graph) interchanging black and white vertices. This, in turn, implies that the Fano plane is self-dual.

The specific representation, on the left, of the Levi graph of the Möbius–Kantor configuration (example 4 above) illustrates that a rotation of {{math|{{pi}}/4}} about the center (either clockwise or counterclockwise) of the diagram interchanges the blue and red vertices and maps edges to edges. That is to say that there exists a color interchanging automorphism of this graph. Consequently, the incidence structure known as the Möbius–Kantor configuration is self-dual.