Various functions which generate vertex layouts for the `gplot3d`

visualization routine.

```
gplot3d.layout.adj(d, layout.par)
gplot3d.layout.eigen(d, layout.par)
gplot3d.layout.fruchtermanreingold(d, layout.par)
gplot3d.layout.geodist(d, layout.par)
gplot3d.layout.hall(d, layout.par)
gplot3d.layout.kamadakawai(d, layout.par)
gplot3d.layout.mds(d, layout.par)
gplot3d.layout.princoord(d, layout.par)
gplot3d.layout.random(d, layout.par)
gplot3d.layout.rmds(d, layout.par)
gplot3d.layout.segeo(d, layout.par)
gplot3d.layout.seham(d, layout.par)
```

d

an adjacency matrix, as passed by `gplot3d`

.

layout.par

a list of parameters.

A matrix whose rows contain the x,y,z coordinates of the vertices of `d`

.

Like `gplot`

, `gplot3d`

allows for the use of arbitrary vertex layout algorithms via the `gplot3d.layout.*`

family of routines. When called, `gplot3d`

searches for a `gplot3d.layout`

function whose third name matches its `mode`

argument (see `gplot3d`

help for more information); this function is then used to generate the layout for the resulting plot. In addition to the routines documented here, users may add their own layout functions as needed. The requirements for a `gplot3d.layout`

function are as follows:

the first argument,

`d`

, must be the (dichotomous) graph adjacency matrix;the second argument,

`layout.par`

, must be a list of parameters (or`NULL`

, if no parameters are specified); andthe return value must be a real matrix of dimension

`c(3,NROW(d))`

, whose rows contain the vertex coordinates.

Other than this, anything goes. (In particular, note that `layout.par`

could be used to pass additional matrices, if needed.)

The `gplot3d.layout`

functions currently supplied by default are as follows:

- eigen
This function places vertices based on the eigenstructure of the adjacency matrix. It takes the following arguments:

- layout.par\$var
This argument controls the matrix to be used for the eigenanalysis.

`"symupper"`

,`"symlower"`

,`"symstrong"`

,`"symweak"`

invoke`symmetrize`

on`d`

with the respective symmetrizing rule.`"user"`

indicates a user-supplied matrix (see below), while`"raw"`

indicates that`d`

should be used as-is. (Defaults to`"raw"`

.)- layout.par\$evsel
If

`"first"`

, the first three eigenvectors are used; if`"size"`

, the three eigenvectors whose eigenvalues have the largest magnitude are used instead. Note that only the real portion of the associated eigenvectors is used. (Defaults to`"first"`

.)- layout.par\$mat
If

`layout.par\$var=="user"`

, this matrix is used for the eigenanalysis. (No default.)

- fruchtermanreingold
This function generates a layout using a variant of Fruchterman and Reingold's force-directed placement algorithm. It takes the following arguments:

- layout.par\$niter
This argument controls the number of iterations to be employed. (Defaults to 300.)

- layout.par\$max.delta
Sets the maximum change in position for any given iteration. (Defaults to

`NROW(d)`

.)- layout.par\$volume
Sets the "volume" parameter for the F-R algorithm. (Defaults to

`NROW(d)^3`

.)- layout.par\$cool.exp
Sets the cooling exponent for the annealer. (Defaults to 3.)

- layout.par\$repulse.rad
Determines the radius at which vertex-vertex repulsion cancels out attraction of adjacent vertices. (Defaults to

`volume*NROW(d)`

.)- layout.par\$seed.coord
A three-column matrix of initial vertex coordinates. (Defaults to a random spherical layout.)

- hall
This function places vertices based on the last three eigenvectors of the Laplacian of the input matrix (Hall's algorithm). It takes no arguments.

- kamadakawai
This function generates a vertex layout using a version of the Kamada-Kawai force-directed placement algorithm. It takes the following arguments:

- layout.par\$niter
This argument controls the number of iterations to be employed. (Defaults to 1000.)

- layout.par\$sigma
Sets the base standard deviation of position change proposals. (Defaults to

`NROW(d)/4`

.)- layout.par\$initemp
Sets the initial "temperature" for the annealing algorithm. (Defaults to 10.)

- layout.par\$cool.exp
Sets the cooling exponent for the annealer. (Defaults to 0.99.)

- layout.par\$kkconst
Sets the Kamada-Kawai vertex attraction constant. (Defaults to

`NROW(d)^3`

.)- layout.par\$elen
Provides the matrix of interpoint distances to be approximated. (Defaults to the geodesic distances of

`d`

after symmetrizing, capped at`sqrt(NROW(d))`

.)- layout.par\$seed.coord
A three-column matrix of initial vertex coordinates. (Defaults to a gaussian layout.)

- mds
This function places vertices based on a metric multidimensional scaling of a specified distance matrix. It takes the following arguments:

- layout.par\$var
This argument controls the raw variable matrix to be used for the subsequent distance calculation and scaling.

`"rowcol"`

,`"row"`

, and`"col"`

indicate that the rows and columns (concatenated), rows, or columns (respectively) of`d`

should be used.`"rcsum"`

and`"rcdiff"`

result in the sum or difference of`d`

and its transpose being employed.`"invadj"`

indicates that`max{d}-d`

should be used, while`"geodist"`

uses`geodist`

to generate a matrix of geodesic distances from`d`

. Alternately, an arbitrary matrix can be provided using`"user"`

. (Defaults to`"rowcol"`

.)- layout.par\$dist
The distance function to be calculated on the rows of the variable matrix. This must be one of the

`method`

parameters to`dist`

(`"euclidean"`

,`"maximum"`

,`"manhattan"`

, or`"canberra"`

), or else`"none"`

. In the latter case, no distance function is calculated, and the matrix in question must be square (with dimension`dim(d)`

) for the routine to work properly. (Defaults to`"euclidean"`

.)- layout.par\$exp
The power to which distances should be raised prior to scaling. (Defaults to 2.)

- layout.par\$vm
If

`layout.par\$var=="user"`

, this matrix is used for the distance calculation. (No default.)

Note: the following layout functions are based on

`mds`

:- adj
scaling of the raw adjacency matrix, treated as similarities (using

`"invadj"`

).- geodist
scaling of the matrix of geodesic distances.

- rmds
euclidean scaling of the rows of

`d`

.- segeo
scaling of the squared euclidean distances between row-wise geodesic distances (i.e., approximate structural equivalence).

- seham
scaling of the Hamming distance between rows/columns of

`d`

(i.e., another approximate structural equivalence scaling).

- princoord
This function places vertices based on the eigenstructure of a given correlation/covariance matrix. It takes the following arguments:

- layout.par\$var
The matrix of variables to be used for the correlation/covariance calculation.

`"rowcol"`

,`"col"`

, and`"row"`

indicate that the rows/cols, columns, or rows (respectively) of`d`

should be employed.`"rcsum"`

`"rcdiff"`

result in the sum or difference of`d`

and`t(d)`

being used.`"user"`

allows for an arbitrary variable matrix to be supplied. (Defaults to`"rowcol"`

.)- layout.par\$cor
Should the correlation matrix (rather than the covariance matrix) be used? (Defaults to

`TRUE`

.)- layout.par\$vm
If

`layout.par\$var=="user"`

, this matrix is used for the correlation/covariance calculation. (No default.)

- random
This function places vertices randomly. It takes the following argument:

- layout.par\$dist
The distribution to be used for vertex placement. Currently, the options are

`"unif"`

(for uniform distribution on the unit cube),`"uniang"`

(for a ``gaussian sphere'' configuration), and`"normal"`

(for a straight Gaussian distribution). (Defaults to`"unif"`

.)

Fruchterman, T.M.J. and Reingold, E.M. (1991). ``Graph Drawing by Force-directed Placement.'' *Software - Practice and Experience,* 21(11):1129-1164.

Kamada, T. and Kawai, S. (1989). ``An Algorithm for Drawing General Undirected Graphs.'' *Information Processing Letters,* 31(1):7-15.