Built-in Mathematica Symbol

GraphPlot3D

GraphPlot3D[{v_i1->v_j1, v_i2->v_j2, ...}]
generates a 3D plot of the graph in which vertex v_ik is connected to vertex v_jk.

GraphPlot3D[{{v_i1->v_j1, lbl₁}, ...}]
associates labels lbl_k with edges in the graph.

GraphPlot[m]
generates a plot of the graph represented by the adjacency matrix m.

GraphPlot3D attempts to place vertices in 3D to give a well laid-out version of the graph.

GraphPlot3D has the same options as Graphics3D, with the following additions and changes:

DataRange	Automatic	the range of vertex coordinates to generate
EdgeRenderingFunction	Automatic	function to give explicit graphics for edges
Method	Automatic	the method used to lay out the graph
MultiedgeStyle	Automatic	how to draw multiple edges between vertices
PackingMethod	Automatic	method to use for packing components
PlotStyle	Automatic	overall graphics directives for vertices and edges
SelfLoopStyle	Automatic	how to draw edges linking a vertex to itself
VertexCoordinateRules	Automatic	rules for explicit vertex coordinates
VertexLabeling	Automatic	whether to show vertex names as labels
VertexRenderingFunction	Automatic	function to give explicit graphics for vertices

With the default setting VertexLabeling->Automatic, vertices are displayed as points, with their names v_k given in tooltips.

With VertexRenderingFunction->f, each vertex is rendered with the 3D graphics primitives given by f[r_k, v_k], where r_k is the position where the vertex is being placed, and v_k is its name.

With EdgeRenderingFunction->g, each edge is rendered with the 3D graphics primitives given by g[{r_i, ..., r_j}, {v_i, v_j}, lbl_ij], where r_i, r_j are the beginning and ending points of the edge, v_i, v_j are the beginning and ending vertices, and lbl_ij is any label specified for the edge.

The graphics primitives obtained by applying EdgeRenderingFunction and VertexRenderingFunction are in effect directly spliced into the 3D graphic generated by GraphPlot3D. Inset can be used to insert an arbitrary expression.

With the default setting DataRange->Automatic, coordinates are chosen so that the average length of the edges in the graph is approximately .

In VertexCoordinateRules, an explicit rule v_k->{x_k, y_k, z_k} specifies coordinates for a vertex. If any coordinate is given as Automatic, it is found automatically. Vertices for which no rules are specified are taken to have automatically generated x, y and z positions.

The graph does not need to be connected. Disconnected components are typically arranged so as to fill a planar area roughly uniformly.

When a graph is specified by an adjacency matrix, the names of its vertices are taken to be successive integers starting at 1.

With the default setting MultiedgeStyle->Automatic, multiple edges are not shown if the graph is specified by an adjacency matrix.

Possible settings for Method include "SpiralEmbedding", "RandomEmbedding", "HighDimensionalEmbedding", "RadialDrawing", "SpringEmbedding" and "SpringElectricalEmbedding".

With Method->Automatic, GraphPlot3D normally uses the "SpringElectricalEmbedding" method, though it uses the "RadialDrawing" method if the graph is a tree.