the point is not on the line, the pair is called an anti-flag. Distance in an incidence structure There is no natural concept of distance (a metric) in an incidence structure. However, a combinatorial metric does exist in the corresponding incidence graph (Levi graph), namely the length of the shortest 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. Partial linear spaces Incidence structures that are most studied are those that satisfy some additional properties (axioms), such as projective planes, affine planes, generalized polygons, partial geometries and near polygons. Very general incidence structures can be obtained by imposing "mild" conditions, such as: A partial linear space is an incidence structure for which the following axioms are true: Every pair of distinct points determines at most one line. Every line contains at least two distinct points. In a partial linear space it is also true that every pair of distinct lines meet in at most one point. This statement does not have to be assumed as it is readily proved from axiom one above. Further constraints are provided by the regularity conditions: RLk: Each line is incident with the same number of points. If finite this number is often denoted by . RPr: Each point is incident with the same number of lines. If finite this number is often denoted by . The second axiom of a partial linear space implies that . Neither regularity condition implies the other, so it has to be assumed that . A finite partial linear space satisfying both regularity conditions with is called a tactical configuration. Some authors refer to these simply as configurations, or projective configurations.