contracts a collection of vertices v1, v2, into a single vertex of the graph g.


contracts several collections of vertices.


uses rules vw to specify the graph g.

Details and Options

  • VertexContract is also known as vertex identification.
  • VertexContract[g,{v1,v2,}] creates a new graph from g by removing all edges between vi and vj and merging them into the single vertex v1.
  • VertexContract works with undirected graphs, directed graphs, multigraphs, and mixed graphs.


open allclose all

Basic Examples  (1)

Contract vertices of a graph:

Scope  (7)

VertexContract works with undirected graphs:

Directed graphs:


Mixed graphs:

Use rules to specify the graph:

Use patterns to specify a set of vertices:

VertexContract works with large graphs:

Applications  (2)

Find the connectivity between communities in a network:

Condensation graph:

List all possible vertex identifications between two RNA tree models to model RNA bonding:

Gather all isomorphic graphs into groups and show non-isomorphic trees:

Properties & Relations  (2)

Using VertexReplace to contract vertices:

EdgeContract can be computed using VertexContract:

Introduced in 2014
Updated in 2015