R: Generate coordinates for plotting graphs

layout {igraph}

R Documentation

Generate coordinates for plotting graphs

Description

Some simple and not so simple functions determining the placement of the vertices for drawing a graph.

Usage

layout.auto(graph, dim=2, ...)
layout.random(graph, params, dim=2)
layout.circle(graph, params)
layout.sphere(graph, params)
layout.fruchterman.reingold(graph, ..., dim=2, params)
layout.kamada.kawai(graph, ..., dim=2, params)
layout.spring(graph, ..., params)
layout.reingold.tilford(graph, ..., params)
layout.fruchterman.reingold.grid(graph, ..., params)
layout.lgl(graph, ..., params)
layout.graphopt(graph, ..., params=list())
layout.svd(graph, d=shortest.paths(graph), ...)
layout.norm(layout, xmin = NULL, xmax = NULL, ymin = NULL, ymax = NULL,
      zmin = NULL, zmax = NULL)

Arguments

`graph`	The graph to place.
`params`	The list of function dependent parameters.
`dim`	Numeric constant, either 2 or 3. Some functions are able to generate 2d and 3d layouts as well, supply this argument to change the default behavior.
`...`	Function dependent parameters, this is an alternative notation to the `params` argument. For `layout.auto` these extra parameters are simply passed to the real layout function, if one is called.
`d`	The matrix used for singular value decomposition. By default it is the distance matrix of the graph.
`layout`	A matrix with two or three columns, the layout to normalize.
`xmin,xmax`	The limits for the first coordinate, if one of them or both are `NULL` then no normalization is performed along this direction.
`ymin,ymax`	The limits for the second coordinate, if one of them or both are `NULL` then no normalization is performed along this direction.
`zmin,zmax`	The limits for the third coordinate, if one of them or both are `NULL` then no normalization is performed along this direction.

Details

These functions calculate the coordinates of the vertices for a graph usually based on some optimality criterion.

layout.auto tries to choose an appropriate layout function for the supplied graph, and uses that to generate the layout. The current implementations works like this:

If the graph has a graph attribute called ‘layout’, then this is used. If this attribute is an R function, then it is called, with the graph and any other extra arguments.
Otherwise, if the graph has vertex attributes called ‘x’ and ‘y’, then these are used as coordinates. If the graph has an additional ‘z’ vertex attribute, that is also used.
Otherwise, if the graph is connected and has less than 100 vertices, the Kamada-Kawai layout is used, by calling layout.kamada.kawai.
Otherwise, if the graph has less than 1000 vertices, then the Fruchterman-Reingold layout is used, by calling layout.fruchterman.reingold.
Otherwise the DrL layout is used, layout.drl is called.

layout.random simply places the vertices randomly on a square. It has no parameters.

layout.circle places the vertices on a unit circle equidistantly. It has no paramaters.

layout.sphere places the vertices (approximately) uniformly on the surface of a sphere, this is thus a 3d layout. It is not clear however what “uniformly on a sphere” means.

layout.fruchterman.reingold uses a force-based algorithm proposed by Fruchterman and Reingold, see references. Parameters and their default values:

niter: Numeric, the number of iterations to perform (500).
coolexp: Numeric, the cooling exponent for the simulated annealing (3).
maxdelta: Maximum change (vcount(graph)).
area: Area parameter (vcount(graph)^2).
repulserad: Cancellation radius (area*vcount(graph)).
weights: A vector giving edge weights or NULL. If not NULL then the attraction along the edges will be multiplied by the given edge weights (NULL).
minx: If not NULL, then it must be a numeric vector that gives lower boundaries for the ‘x’ coordinates of the vertices. The length of the vector must match the number of vertices in the graph.
maxx: Similar to minx, but gives the upper boundaries.
miny: Similar to minx, but gives the lower boundaries of the ‘y’ coordinates.
maxy: Similar to minx, but gives the upper boundaries of the ‘y’ coordinates.
minz: Similar to minx, but gives the lower boundaries of the ‘z’ coordinates, if the dim argument is 3. Otherwise it is ignored.
maxz: Similar to minx, but gives the upper boundaries of the ‘z’ coordinates, if the dim argument is 3. Otherwise it is ignored.
start: If given, then it should be a matrix with two columns and one line for each vertex. This matrix will be used as starting positions for the algorithm. If not given, then a random starting matrix is used.

This function was ported from the SNA package.

layout.kamada.kawai is another force based algorithm. Parameters and default values:

niter: Number of iterations to perform (1000).
sigma: Sets the base standard deviation of position change proposals (vcount(graph)/4).
initemp: The initial temperature (10).
coolexp: The cooling exponent (0.99).
kkconst: Sets the Kamada-Kawai vertex attraction constant (vcount(graph)**2).
minx: If not NULL, then it must be a numeric vector that gives lower boundaries for the ‘x’ coordinates of the vertices. The length of the vector must match the number of vertices in the graph.
maxx: Similar to minx, but gives the upper boundaries.
miny: Similar to minx, but gives the lower boundaries of the ‘y’ coordinates.
maxy: Similar to minx, but gives the upper boundaries of the ‘y’ coordinates.
minz: Similar to minx, but gives the lower boundaries of the ‘z’ coordinates, if the dim argument is 3. Otherwise it is ignored.
maxz: Similar to minx, but gives the upper boundaries of the ‘z’ coordinates, if the dim argument is 3. Otherwise it is ignored.
start: If given, then it should be a matrix with two columns and one line for each vertex. This matrix will be used as starting positions for the algorithm. If not given, then a random starting matrix is used.

This function performs very well for connected graphs, but it gives poor results for unconnected ones. This function was ported from the SNA package.

layout.spring is a spring embedder algorithm. Parameters and default values:

mass: The vertex mass (in ‘quasi-kilograms’). (Defaults to 0.1.)
equil: The equilibrium spring extension (in ‘quasi-meters’). (Defaults to 1.)
k: The spring coefficient (in ‘quasi-Newtons per quasi-meter’). (Defaults to 0.001.)
repeqdis: The point at which repulsion (if employed) balances out the spring extension force (in ‘quasi-meters’). (Defaults to 0.1.)
kfr: The base coefficient of kinetic friction (in ‘quasi-Newton quasi-kilograms’). (Defaults to 0.01.)
repulse: Should repulsion be used? (Defaults to FALSE.)

This function was ported from the SNA package.

layout.reingold.tilford generates a tree-like layout, so it is mainly for trees. Parameters and default values:

root: The id of the root vertex, defaults to 1.
circular: Logical scalar, whether to plot the tree in a circular fashion, defaults to FALSE.
flip.y: Logical scalar, whether to flip the ‘y’ coordinates. The default is flipping because that puts the root vertex on the top.

layout.fruchterman.reingold.grid is similar to layout.fruchterman.reingold but repelling force is calculated only between vertices that are closer to each other than a limit, so it is faster. Patameters and default values:

niter: Numeric, the number of iterations to perform (500).
maxdelta: Maximum change for one vertex in one iteration. (The number of vertices in the graph.)
area: The area of the surface on which the vertices are placed. (The square of the number of vertices.)
coolexp: The cooling exponent of the simulated annealing (1.5).
repulserad: Cancellation radius for the repulsion (the area times the number of vertices).
cellsize: The size of the cells for the grid. When calculating the repulsion forces between vertices only vertices in the same or neighboring grid cells are taken into account (the fourth root of the number of area.
start: If given, then it should be a matrix with two columns and one line for each vertex. This matrix will be used as starting positions for the algorithm. If not given, then a random starting matrix is used.

layout.lgl is for large connected graphs, it is similar to the layout generator of the Large Graph Layout software (http://lgl.sourceforge.net/). Parameters and default values:

maxiter: The maximum number of iterations to perform (150).
maxdelta: The maximum change for a vertex during an iteration (the number of vertices).
area: The area of the surface on which the vertices are placed (square of the number of vertices).
coolexp: The cooling exponent of the simulated annealing (1.5).
repulserad: Cancellation radius for the repulsion (the area times the number of vertices).
cellsize: The size of the cells for the grid. When calculating the repulsion forces between vertices only vertices in the same or neighboring grid cells are taken into account (the fourth root of the number of area.
root: The id of the vertex to place at the middle of the layout. The default value is -1 which means that a random vertex is selected.

layout.graphopt is a port of the graphopt layout algorithm by Michael Schmuhl. graphopt version 0.4.1 was rewritten in C and the support for layers was removed (might be added later) and a code was a bit reorganized to avoid some unneccessary steps is the node charge (see below) is zero.

graphopt uses physical analogies for defining attracting and repelling forces among the vertices and then the physical system is simulated until it reaches an equilibrium. (There is no simulated annealing or anything like that, so a stable fixed point is not guaranteed.)

See also http://www.schmuhl.org/graphopt/ for the original graphopt.

Parameters and default values:

niter: Integer scalar, the number of iterations to perform. Should be a couple of hundred in general. If you have a large graph then you might want to only do a few iterations and then check the result. If it is not good enough you can feed it in again in the start argument. The default value is 500.
charge: The charge of the vertices, used to calculate electric repulsion. The default is 0.001.
mass: The mass of the vertices, used for the spring forces. The default is 30.
spring.length: The length of the springs, an integer number. The default value is zero.
spring.constant: The spring constant, the default value is one.
max.sa.movement: Real constant, it gives the maximum amount of movement allowed in a single step along a single axis. The default value is 5.
start: If given, then it should be a matrix with two columns and one line for each vertex. This matrix will be used as starting positions for the algorithm. If not given, then a random starting matrix is used.

layout.svd is a currently experimental layout function based on singular value decomposition. It does not have the usual params argument, but take a single argument, the distance matrix of the graph. This function generates the layout separately for each graph component and then merges them via layout.merge.

layout.norm normalizes a layout, it linearly transforms each coordinate separately to fit into the given limits.

layout.drl is another force-driven layout generator, it is suitable for quite large graphs. See layout.drl for details.

Value

All these functions return a numeric matrix with at least two columns and the same number of lines as the number of vertices.

Author(s)

Gabor Csardi csardi.gabor@gmail.com

References

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.

Reingold, E and Tilford, J (1981). Tidier drawing of trees. IEEE Trans. on Softw. Eng., SE-7(2):223–228.

Examples

g <- graph.ring(10)
layout.random(g)
layout.kamada.kawai(g)

# Fixing ego
g <- ba.game(20, m=2)
minC <- rep(-Inf, vcount(g))
maxC <- rep(Inf, vcount(g))
minC[1] <- maxC[1] <- 0
co <- layout.fruchterman.reingold(g, minx=minC, maxx=maxC,
                                  miny=minC, maxy=maxC)
co[1,]
## Not run: plot(g, layout=co, vertex.size=30, edge.arrow.size=0.2,
     vertex.label=c("ego", rep("", vcount(g)-1)), rescale=FALSE,
     xlim=range(co[,1]), ylim=range(co[,2]), vertex.label.dist=1,
     vertex.label.color="red")
axis(1)
axis(2)

## End(Not run)

[Package igraph version 0.7.0 Index]