The incidence matrix is an important tool in the theory of block designs.

The incidence matrix for the Fano plane looks like this:

Another matrix representation for a graph is the incidence matrix.

The incidence matrix contains all the information that is known about an incidence geometry.

The following incidence matrix is that of a triangle:

If we look at the incidence matrix, we see that the sum of each column is equal to 2.

The line-line matrix can be obtained from the incidence matrix.

In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects.

Any two incidence matrices are related by negating some subset of the columns.

Incidence matrices are mostly used in graph theory.

The definitions of incidence matrix apply to graphs with loops and multiple edges.

Thus the corresponding incidence matrix of this abstract polytope may be shown as:

Hypergraphs can be characterised by their incidence matrices.

It provides a partial classification of non-trivial irreducible incidence matrices.

The matrix E is called the incidence matrix.

It affects the incidence matrix by negating the rows of the switched vertices.

In this accumulated incidence matrix representation the diagonal entries represent the total counts of either element type.

All oriented incidence matrices of G differ only by negating some set of columns.

In many uses, this is an insignificant difference, so one can speak of 'the' oriented incidence matrix, even though that is technically incorrect.

Negating a row of the incidence matrix corresponds to switching the corresponding vertex.

In fact, the incidence matrix is an alternative mathematical representation of the graph which dispenses with the need for any kind of drawing.

Any incidence matrix with more than two non-zero entries in any row is a representation of a hypergraph.

It is the incidence matrix of any bidirected graph that orients the given signed graph.

The incidence matrix is an n-by-m matrix.

Let S denote the sum of the entries in the first m columns of the incidence matrix: