This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

AdjacencyMatrix

AdjacencyMatrix[g]
gives the SparseArray object representing the graph g.

gives the SparseArray object representing the graph g, adding additional unconnected vertices, if necessary, to create a graph with n vertices.
  • The graph g can be specified by a rule list, an adjacency matrix, or the Combinatorica representation of a graph.
  • The rows/columns of the SparseArray object correspond to vertices in the order returned by VertexList[g].
The SparseArray representation of a graph specified by a rule list:
This gives a SparseArray representation of a graph specified by a Combinatorica object:
This adds an extra row and column to the adjacency matrix, corresponding to unconnected vertices:
Needs["GraphUtilities`"]
The SparseArray representation of a graph specified by a rule list:
In[2]:=
Click for copyable input
Out[2]//MatrixForm=
 
Needs["GraphUtilities`"]
This gives a SparseArray representation of a graph specified by a Combinatorica object:
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]//MatrixForm=
 
Needs["GraphUtilities`"]
This adds an extra row and column to the adjacency matrix, corresponding to unconnected vertices:
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]//MatrixForm=
In[4]:=
Click for copyable input
Out[4]=
This shows the MatrixPlot of the adjacency matrix of a GridGraph, and its graph drawing:
A second argument specifying fewer vertices than those contained in the graph is ignored: