# Vertex Layout Functions for plot.network

### Description

Various functions which generate vertex layouts for the `plot.network`

visualization routine.

### Usage

1 2 3 | ```
network.layout.circle(nw, layout.par)
network.layout.fruchtermanreingold(nw, layout.par)
network.layout.kamadakawai(nw, layout.par)
``` |

### Arguments

`nw` |
a network object, as passed by |

`layout.par` |
a list of parameters. |

### Details

Vertex layouts for network visualization pose a difficult problem – there is no single, “good” layout algorithm, and many different approaches may be valuable under different circumstances. With this in mind, `plot.network`

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

family of routines. When called, `plot.network`

searches for a `network.layout`

function whose fourth name matches its `mode`

argument (see `plot.network`

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 `network.layout`

function are as follows:

the first argument,

`nw`

, must be a network object;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(2,network.size(nw))`

, whose rows contain the vertex coordinates.

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

could be used to pass additional matrices or other information, if needed. Alternately, it is possible to make layout methods that respond to covariates on the network object, which are maintained intact by plot.network.)

The `network.layout`

functions currently supplied by default are as follows (with `n==network.size(nw)`

):

- circle
This function places vertices uniformly in a circle; it takes no arguments.

- 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. Larger values take longer, but will provide a more refined layout. (Defaults to 500.)

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

`n`

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

`n^2`

.)- 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

`area*log(n)`

.)- layout.par\$ncell
To speed calculations on large graphs, the plot region is divided at each iteration into

`ncell`

by`ncell`

“cells”, which are used to define neighborhoods for force calculation. Moderate numbers of cells result in fastest performance; too few cells (down to 1, which produces “pure” F-R results) can yield odd layouts, while too many will result in long layout times. (Defaults to`n^0.4`

.)- layout.par\$cell.jitter
Jitter factor (in units of cell width) used in assigning vertices to cells. Small values may generate “grid-like” anomalies for graphs with many isolates. (Defaults to

`0.5`

.)- layout.par\$cell.pointpointrad
Squared “radius” (in units of cells) such that exact point interaction calculations are used for all vertices belonging to any two cells less than or equal to this distance apart. Higher values approximate the true F-R solution, but increase computational cost. (Defaults to

`0`

.)- layout.par\$cell.pointcellrad
Squared “radius” (in units of cells) such that approximate point/cell interaction calculations are used for all vertices belonging to any two cells less than or equal to this distance apart (and not within the point/point radius). Higher values provide somewhat better approximations to the true F-R solution at slightly increased computational cost. (Defaults to

`18`

.)- layout.par\$cell.cellcellrad
Squared “radius” (in units of cells) such that approximate cell/cell interaction calculations are used for all vertices belonging to any two cells less than or equal to this distance apart (and not within the point/point or point/cell radii). Higher values provide somewhat better approximations to the true F-R solution at slightly increased computational cost. Note that cells beyond this radius (if any) do not interact, save through edge attraction. (Defaults to

`ncell^2`

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

- 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

`n/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

`n)^2`

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

`nw`

after symmetrizing, capped at`sqrt(n)`

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

### Value

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

.

### Note

The `network.layout`

routines shown here are adapted directly from the `gplot.layout`

routines of the `sna`

package.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

Butts, C. T. (2008). “network: a Package for Managing Relational Data in R.” *Journal of Statistical Software*, 24(2). http://www.jstatsoft.org/v24/i02/

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.

### See Also

`plot.network`