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

adjacencyMatrix -- returns the adjacency Matrix of a graph

Synopsis

Description

This function returns the adjacency matrix of the given graph G. The (i,j)^{th} position of the matrix is 1 if there is an edge between the i^{th} vertex and j^{th} vertex, and 0 otherwise. The rows and columns are indexed by the variables of the ring and use the ordering of the variables for determining the order of the rows and columns.

i1 : S = QQ[a..f];
 
i2 : G = graph {a*b,a*c,b*c,c*d,d*e,e*f,f*a,a*d}

o2 = Graph{"edges" => {{a, b}, {a, c}, {b, c}, {a, d}, {c, d}, {d, e}, {a, f}, {e, f}}}
           "ring" => S
           "vertices" => {a, b, c, d, e, f}

o2 : Graph
 
i3 : t = adjacencyMatrix G

o3 = | 0 1 1 1 0 1 |
     | 1 0 1 0 0 0 |
     | 1 1 0 1 0 0 |
     | 1 0 1 0 1 0 |
     | 0 0 0 1 0 1 |
     | 1 0 0 0 1 0 |

              6       6
o3 : Matrix ZZ  <-- ZZ
 
i4 : T = QQ[f,e,d,c,b,a];
 
i5 : G = graph {a*b,a*c,b*c,c*d,d*e,e*f,f*a,a*d}

o5 = Graph{"edges" => {{f, e}, {e, d}, {d, c}, {c, b}, {f, a}, {d, a}, {c, a}, {b, a}}}
           "ring" => T
           "vertices" => {f, e, d, c, b, a}

o5 : Graph
 
i6 : t = adjacencyMatrix G -- although the same graph, matrix is different since variables have different ordering

o6 = | 0 1 0 0 0 1 |
     | 1 0 1 0 0 0 |
     | 0 1 0 1 0 1 |
     | 0 0 1 0 1 1 |
     | 0 0 0 1 0 1 |
     | 1 0 1 1 1 0 |

              6       6
o6 : Matrix ZZ  <-- ZZ

See also

Ways to use adjacencyMatrix:

For the programmer

The object adjacencyMatrix is a method function.