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networks[draw3d] - draw an undirected connected graph in 3-D

Calling Sequence

draw3d(G, opts )

Parameters

G

-

undirected graph

opts

-

(optional) plot options; see plot3d[option]

Description

• 

Important: The networks package has been deprecated.  Use the superseding package GraphTheory instead.

• 

The draw3d(G, opts) routine draws an undirected connected graph G=V,E in three dimensions in such a way that structure and symmetry in the graph is revealed.  The graph G is input as a GRAPH data type as created in the networks package. The output is a three dimensional plot of labeled points with lines connecting them.  The points correspond to the vertices in the graph and the lines correspond to the edges in the graph.

• 

The location of the vertices of the graph is determined as follows. Let A be the adjacency matrix of G and let u, v and w be three eigenvectors of A with corresponding second, third, and fourth largest eigenvalue in absolute value.  Then the (x,y,z) coordinates of the ith vertex of G is (ui,vi,wi).

• 

Sometimes other symmetries in the graph can be seen by using other eigenvectors. If the optional argument eigenvectors=e1,e2,e3 is specified, where e1, e2, and e3 are vertex numbers (integers from 1 through the number of vertices), the eigenvectors corresponding to the eigenvalues of these relative magnitudes are used.

• 

If the graph is not connected, you can draw the connected components separately.  The last example below shows how to do this.

• 

Remaining arguments are interpreted as options which are specified as equations of the form option = value. The remaining options are the same as those available for the plot3d command. For more information, see plot3d[option].

• 

The algorithm used is the same as that described for plots[graphplot3d(deprecated)]. The networks[draw3d] and plots[graphplot3d] commands are identical except they accept different forms of graph input.

• 

Note: The plots[graphplot3d(deprecated)] command has been superseded by GraphTheory[DrawGraph].

Examples

Important: The networks package has been deprecated.  Use the superseding package GraphTheory instead.

withnetworks:

G:=cube:

draw3dG

A:=adjacencyG

cp:=factorlinalg[charpoly]A,x

draw3dG,eigenvectors=1,3,8

G:=dodecahedron:

draw3dG,title=A dodecahedron

An example of a graph that is not connected.

V:=seqi,i=0..8:

E:=7,8,2,7,0,6,5,7,1,2,1,5,2,4,0,3,1,8,3,6,4,8,4,5:

G:=graphV,E:

draw3dG

C:=componentsG

The number of connected components:

nopsC

C1:=induceC1,G:

C2:=induceC2,G:

draw3dC1

draw3dC2

See Also

GraphTheory, GraphTheory[DrawGraph], GraphTheory[DrawNetwork], networks(deprecated)[draw], networks(deprecated)[induce], plot3d[option], plots[graphplot3d(deprecated)]


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