Geometry

Definition with symbols
An incidence system $$(G,*,t,\Phi)$$ is termed a geometry if it satisfies the following additional conditions:


 * Every maximal flag contains exactly one element of each type, viz every maximal flag has corank 0
 * For any two distinct types, the bipartite graph on the union of elements of those types given by the incidence relation, is a connected graph

Graph-theoretic definition
An incidence system is termed a geometry if the corresponding graph has the following properties:


 * Every maximal clique in it has one vertex from each part
 * The subgraph induced on any two parts is connected.

Weaker properties

 * Connected incidence system
 * Incidence system