Vertex space

In the mathematical discipline of graph theory the vertex space for a finite undirected graph is vector space structure on the vertex set of the graph, making it possible to use linear algebra for studying the graph.

Definition

Given a finite undirected graph G: = (V,E) with n vertices, the vertex space is a n-dimensional vector space over . The elements of the vector space are linear combination of vertices of G with addition defined as the symmetric difference.

Properties

The transposed incidence matrix H^T for a graph G defines a linear transformation

between the vertex space and the edge space of G.

See also

• edge space