[1][2] From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line.

They are named for Friedrich Wilhelm Levi, who wrote about them in 1942.

Conversely any bipartite graph with girth at least six can be viewed as the Levi graph of an abstract incidence structure.

[4] Levi graphs may also be defined for other types of incidence structure, such as the incidences between points and planes in Euclidean space.

For every Levi graph, there is an equivalent hypergraph, and vice versa.