Editing Incidence structure (section)

==Generalization==
It is possible to generalize the notion of an incidence structure to include more than two types of objects. A structure with {{mvar|k}} types of objects is called an ''incidence structure of rank'' {{mvar|k}} or a ''rank'' {{mvar|k}} ''geometry''.<ref name=Pisanski158 /> Formally these are defined as {{math|''k'' + 1}} tuples {{math|1= ''S'' = (''P''<sub>1</sub>, ''P''<sub>2</sub>, ..., ''P''<sub>k</sub>, ''I'')}} with {{math|1=''P''<sub>''i''</sub> ∩ ''P''<sub>''j''</sub> = ∅}} and
<math display="block">I \subseteq \bigcup_{i < j} P_i \times P_j.</math>

The Levi graph for these structures is defined as a [[multipartite graph]] with vertices corresponding to each type being colored the same.