Macaulay2 » Documentation
Packages » Graphs :: adjacencyMatrix
next | previous | forward | backward | up | index | toc

adjacencyMatrix -- Returns the adjacency matrix of a Graph or Digraph

Synopsis

Description

The adjacency matrix is the n by n matrix (where n is the number of vertices in graph/digraph G) with rows and columns indexed by the vertices of G. Entry A_(u,v) is 1 if and only if {u,v} is an edge of G and 0 otherwise. It is easy to observe that if we just use a simple graph G, then its adjacency matrix must be symmetric, but if we use a digraph, then it is not necessarily symmetric.

i1 : D = digraph({{1,2},{2,3},{3,4},{4,3}},EntryMode=>"edges");
 
i2 : adjacencyMatrix D

o2 = | 0 1 0 0 |
     | 0 0 1 0 |
     | 0 0 0 1 |
     | 0 0 1 0 |

              4       4
o2 : Matrix ZZ  <-- ZZ
 
i3 : G = graph({1,2,3,4}, {{1,2},{2,3},{3,4},{4,3}})

o3 = Graph{1 => {2}   }
           2 => {1, 3}
           3 => {2, 4}
           4 => {3}

o3 : Graph
 
i4 : adjacencyMatrix G

o4 = | 0 1 0 0 |
     | 1 0 1 0 |
     | 0 1 0 1 |
     | 0 0 1 0 |

              4       4
o4 : Matrix ZZ  <-- ZZ

See also

Ways to use adjacencyMatrix :

For the programmer

The object adjacencyMatrix is a method function.