gives the subgraph of the graph g generated by the vertices vi.
gives the subgraph generated by the edges ej.
gives the subgraph generated by the vertices and edges that match the pattern patt.
uses rules vw to specify the graph g.
Details and Options
- The subgraph generated by the vertices v1,v2,… includes the vertices vi and all edges connecting them in the original graph g.
- The subgraph generated by the edges e1,e2,… includes the edges ej and all edges connecting vertices vi of ej in the original graph g.
- Subgraph works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Examplesopen allclose all
Basic Examples (1)
Give a subgraph of a complete graph:
Highlight the subgraph within the main graph:
Subgraph works with undirected graphs:
Use rules to specify the graph:
Use patterns to select subgraphs:
Find the subgraph with edges that are incident to 3:
Find the subgraph with vertices less than 6:
Subgraph works with large graphs:
Select random subgraphs of size 5:
Find all the subgraphs of the graph g that are isomorphic to the graph h:
Enumerate all subsets of vertices that have the same number of vertices as h:
Select the subgraphs that are isomorphic to h:
Properties & Relations (3)
The vertices of subgraphs are subsets of the original vertices:
The edges of subgraphs are subsets of the original edges:
The subgraph of a complete graph is a complete graph:
Neat Examples (1)
Subtract random neighborhoods from a grid:
Introduced in 2010
Updated in 2014