Incidence matrix Guide, Meaning , Facts, Information and Description

In mathematics, the incidence matrix of an undirected graph G is a p × q matrix where p and q are the number of vertices and edgess respectively, such that if the vertex and edge are incident and 0 otherwise.

The incidence matrix of a directed graph G isa p × q matrix where p and q are the number of vertices and edgess respectively, such that if the edge leaves vertex , if it enters vertex and 0 otherwise.

The incidence matrix is related to the adjacency matrix of a graph by the following theorem:

where and are the adjacency matrix and incidence matrix respectively and is the identity matrix of dimension q.

The cycle space of a graph is equal to the null space of its incidence matrix.

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