Editing Incidence geometry (section)

===Distance in an incidence structure===
There is no natural concept of distance (a [[Metric (mathematics)|metric]]) in an incidence structure. However, a combinatorial metric does exist in the corresponding [[Levi graph|incidence graph (Levi graph)]], namely the length of the shortest [[Path (graph theory)|path]] between two vertices in this [[bipartite graph]]. The distance between two objects of an incidence structure – two points, two lines or a point and a line – can be defined to be the distance between the corresponding vertices in the incidence graph of the incidence structure.

Another way to define a distance again uses a graph-theoretic notion in a related structure, this time the ''collinearity graph'' of the incidence structure. The vertices of the collinearity graph are the points of the incidence structure and two points are joined if there exists a line incident with both points. The distance between two points of the incidence structure can then be defined as their distance in the collinearity graph.

When distance is considered in an incidence structure, it is necessary to mention how it is being defined.