and define a matrix A by
This matrix A is the so called incidence matrix of the incidence structure . Of course, the incidence matrix depends on the enumerations of points and lines chosen. When using the same enumerations as above, the incidence matrix of the dual incidence structure is the transpose At of A.
The matrix AAt is the adjacency matrix, its entry at an off diagonal position (i,j) is the number of lines connecting the two points and .