Package {multigraph}

Plot and Manipulate Multigraphs

Description

Functions to create and network manipulate multigraphs, bipartite graphs, multilevel graphs, and semigroup Cayley colour graphs.

Details

The multigraph package provides functions for plotting complex network structures, including dichotomous and valued graphs. For one-mode data, multigraph displays signed and valued multigraphs with loops, whereas bmgraph represents bipartite graphs for affiliation networks. The mlgraph function visualizes multilevel graphs that “combine” one- and two-mode network data. Cayley colour graphs are drawn with ccgraph to depict relations among ties in multiplex networks encoded in the associated algebraic semigroup structure.

Author(s)

J. Antonio Rivero Ostoic

Maintainer: Antonio Rivero Ostoic <multiplex@post.com>

References

Ostoic, J.A.R. Algebraic Analysis of Social Networks: Models, Methods and Applications Using R, Wiley, 2021
Ostoic, J.A.R. “Algebraic Analysis of Multiple Social Networks with multiplex.” Journal of Statistical Software, 91(11), 1-41. <doi:10.18637/jss.v092.i11>

See Also

multiplex-package, incubs, read.dl, read.gml, transf, edgel, zbind, semigroup

Bipartite Graphs for Affiliation Networks

Description

A function to create and manipulate bipartite graphs for affiliation or two-mode network networks.

Usage

bmgraph(net, layout = c("bip", "bip3", "bip3e", "bipc", "CA", "force", "rand", "stress", 
        "circ", "conc", "circ2"), scope, coord, alpha = c(1, 1, 1), showLbs, showAtts, 
        att = NULL, lbat = "1", main = NULL, cex.main, col.main, font.main, directed, 
        valued, collRecip, cex, pos, lwd, lty, col, ecol, vcol, vcol0, bg, asp, 
        seed = NULL, maxiter = 100, bwd, clu, pch, rot, mirrorX, mirrorY, mirrorV, 
        mirrorH, hds, vedist, jitter, sort, add, adc, perm, ffamily, fstyle, fsize, fcol, 
        mar, scl, new, ...)

Arguments

Details

Bipartite graphs serve as visual aids for affiliation or two-mode networks. While affiliation networks are typically represented as data frames, they can also be visualized using three-dimensional arrays. In such case, each level corresponds to a specific type of connection, resulting in parallel edges within the bipartite graph. Additionally, a bipartite network can be generated using a force-directed algorithm to create a visual representation.

With bipartite graphs consisting of two sets of vertices, clustering information, such as vertex colours, can be stored in a list vclu with two vectors, one for each vertex set. It is possible to group all members of a vertex set into a single class by setting the corresponding vector to NULL.

Value

A plot of the two-mode network as a bipartite graph or multigraph with a projection.

See Also

multigraph, frcd, stsm, conc

Examples

# Two binary relations among three elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 3 ) )

# Plot network as bipartite graph
bmgraph(arr)

# Apply force directed algorithm for plot
bmgraph(arr, layout = "force")

# Apply Correspondence Analysis
bmgraph(arr, layout = "CA", asp = NA)

internal function

Description

internal function

internal function

Description

internal function

Cayley Colour Graph

Description

A function to create and manipulate Cayley colour graphs of semigroup structures.

Usage

ccgraph(x, main = NULL, seed = 0, maxiter = 100, alpha = c(1, 1, 1), 
        scope, loops, collRecip, undRecip, showLbs, cex.main, col.main, font.main, 
        conc, coord, clu, cex, lwd, pch, lty, bwd, bwd2, att, bg, mar, pos, asp, 
        ecol, vcol, vcol0, lbs, col, lbat, swp, swp2, rot, vedist, vldist, 
        mirrorX, mirrorY, mirrorD, mirrorL, mirrorV, mirrorH, ffamily, fstyle, 
        fsize, fcol, scl, hds, nr, gens, flip, ...)

Arguments

Details

The Cayley colour graph is a graphical representation of the relationships among relations in the relational structure of a given multiplex network. Both nodes and directed edges represent string relations, and each shape and colour corresponds to a specific generator relation of the semigroup structure.

Value

A plot of the semigroup or group structure.

See Also

semigroup, multigraph, frcd, conc

Examples

# Create an abstract semigroup from random data
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 1 ) )

S <- semigroup(arr)

# plot semigroup Cayley graph
ccgraph(S)

Concentric Layout

Description

A function to compute the graph coordinated system with a concentric layout.

Usage

conc(net, nr, irot, inv, iflip, mirror = c("N", "X", "Y", "D", "L"), ...)

Arguments

Details

An “Euclidean plane” computes the coordinated system with a concentric layout with at least two radii (unless n = 1). In case that the number of radii is not specified in nr, approx. half of the vertices are located at one radius and half in another one.

The clustering of the actors may be used to establish the location of the vertices in different radii as a numerical, character, or a factor vector.

Value

A data frame with a coordinated system with two columns representing the abscissa and the ordinate in a two-dimensional rectangular Cartesian coordinate system.

See Also

multigraph, bmgraph, frcd, stsm

Examples

# Two binary relations among three elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 3 ) )

# Coordinates for the concentric layout with two radii
coord <- conc(arr, nr = 2)

# Plot multigraph with customized coordinates
multigraph(arr, coord = coord)

Force Directed Layout

Description

A function to compute the graph coordinated system with a force directed layout algorithm.

Usage

frcd(net, seed = seed, maxiter, drp, scl, mov, ...)

Arguments

Details

This function is meant as an internal routine for graph visualization with a force-directed layout procedure. However, it can be used to set the coordinate system with the coord option in functions multigraph and in bmgraph. In such case, the coordinate system of the graph starts with a random displacement of nodes where NULL in the seed argument implies an initial seed based on the computer clock watch, and the number of iterations in maxiter is 60+n.

Value

A data frame with a coordinated system with two columns representing the abscissa and the ordinate in a two-dimensional rectangular Cartesian coordinate system.

References

Fruchterman, T.M.J., & Reingold, E.M. Graph drawing by force-directed placement. Software-Practice & Experience, 21(11), 1129-1164. 1991.

See Also

multigraph, bmgraph, stsm, conc

Examples

# Two binary relations among three elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 3 ) )

# Coordinates for the force directed layout with random start
coord <- frcd(arr, seed = NULL)

# Plot multigraph with forced directed coordinates
multigraph(arr, coord = coord)

internal function

Description

internal function

internal function

Description

internal function

internal function

Description

internal function

Multilevel Graph

Description

A function to create and manipulate multilevel graphs.

Usage

mlgraph(net, layout = c("circ", "force", "stress", "rand", "conc", "bip"), main = NULL, 
        seed = NULL, maxiter = 100, directed = TRUE, alpha = c(1, 1, 1), scope, collRecip, 
        lbs, showLbs, showAtts, cex.main, col.main, font.main, coord, clu, cex, lwd, pch, 
        lty, bwd, bwd2, att, bg, mar, pos, asp, ecol, vcol, vcol0, col, lbat, loops, rot, 
        mirrorX, mirrorY, mirrorD, mirrorL, mirrorV, mirrorH, hds, scl, vedist, vldist, 
        flip, ffamily, fstyle, fsize, fcol, valued, modes, elv, lng, nr, new, jitter, ...)

Arguments

Details

Multilevel graphs represent networks with multiple “levels”, such as distinct domains within a network structure. These networks may include ties both within and between domains.

Because this function accepts many arguments, they may be collected in a list and supplied through the scope option. The list can contain vectors, scalars, or combinations of both for rendering.

The bundle widths bwd and bwd2 range from 0, where edges are collapsed, to the default value of 1, depending on vertex size. Values greater than one are allowed when valued option is used.

In multilevel structures, argument clu serves to assign network members to classes. Setting the corresponding vector to NULL places all members of a domain or codomain in a single class. Likewise, setting argument nr to NULL in the conc layout uses two radii, one for each domain.

Value

A plot of the multilevel graph structure for the network.

See Also

mlvl, multigraph, bmgraph, frcd, stsm, conc

Multigraphs and Valued Multigraphs

Description

A function to create and manipulate multigraphs and valued multigraphs with different layout options.

Usage

multigraph(net, layout = c("circ", "force", "stress", "conc", "rand"), scope, 
           directed = TRUE, loops, signed, valued, values, lbs, showLbs, att, 
           lbat, showAtts, main = NULL, cex.main, col.main, font.main, coord, 
           collRecip, undRecip, seed = NULL, maxiter = 100, clu, cex, cex2, 
           pch, lwd, lty, vcol, vcol0, col, ecol, bwd, bwd2, pos, bg, bg2, asp, 
           drp, add, swp, swp2, flip, alpha = c(1, 1, 1, 1), rot, mirrorX, 
           mirrorY, mirrorD, mirrorL, mirrorV, mirrorH, scl, hds, vedist, 
           vldist, mar, ffamily, fstyle, fsize, fsize2, fcol, fcol2, lclu, sel, 
           new, mai, lscl, rm.isol, nr, jitter, ...)

Arguments

Details

Multigraphs contain parallel edges that represent different relation types within a network. By default, the function uses a circular layout in which tie types are distinguished by shape and a grey colour scale. For undirected multigraphs, reciprocal relations are collapsed automatically, although this behaviour can be disabled. Vertex symbols and colours can be combined by assigning each network member to a class through the clustering option. Vertex sizes can also be specified with a vector whose length matches the network order.

Because the function accepts many arguments, these may be collected in a list and supplied through the scope option. The list may include vectors, lists, scalars, or combinations of these to describe graph characteristics.

The bundle width bwd, and bwd2 for loops, ranges from 0, where edges are collapsed, to the default value of 1, depending on vertex size. Values above one are allowed when the valued option is used. For large or dense networks, argument vedist adjusts the distance between vertices and edges.

For some applications, such as dynamic networks, the ordering of clustering “levels” in clu must be specified; this is done with argument lclu.

If coordinates are supplied, the layout option is ignored.

When argument new is used to plot a graph with a background image, previous plots may need to be initialized with package functions equivalent to graphics::plot.new().

Value

A plot of the network as a multigraph or a valued multigraph.

See Also

bmgraph, ccgraph, frcd, stsm, conc

Examples

# Two binary relations among three elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 3 ) )

# Plot multigraph of this network
multigraph(arr)

# Plot with a force directed algorithm
multigraph(arr, layout = "force")

# As valued graph
multigraph(arr, valued = TRUE)

# As signed graph
multigraph(arr, signed = TRUE)

# With loops and custumized vertex size
multigraph(arr, cex = 3, loops = TRUE)

internal function

Description

internal function

internal function

Description

internal function

internal function

Description

internal function

internal function

Description

internal function

Stress Majorization Layout

Description

A function to compute the graph coordinated system with a stress majorization layout algorithm.

Usage

stsm(net, seed = seed, maxiter = 40, drp, jitter, method, ...)

Arguments

Details

Like the function frcd, this routine serves as an internal tool for graph visualization. It is also designed to establish the coordinate system using the coord option within the multigraph and bmgraph functions.

In this scenario, the graph's coordinate system commences with nodes randomly positioned, and if NULL is entered in the seed argument. An initial seed will be generated based on the computer clock watch where the number of iterations in maxiter is 40.

Value

A data frame with a coordinated system with two columns representing the abscissa and the ordinate in a two-dimensional rectangular Cartesian coordinate system.

References

Gansner, E.R., Koren, Y., & North, S. Graph drawing by stress majorization. In Graph Drawing 2004: 12th International Symposium, New York, NY, USA, revised selected papers. Springer. pp. 239-250. 2005.

See Also

multigraph, bmgraph, frcd, conc

Examples

# Two binary relations among three elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 3 ) )

# Coordinates for stress majorization layout with random start
coord <- stsm(arr, seed = NULL)

# Plot multigraph with stress majorization coordinates
multigraph(arr, coord = coord)

External Datasets in dl Format.

Description

External datasets in multigraph package are for illustration purposes, and they have a Ucinet dl format. The four datasets need to be transformed with function read.dl from multiplex package for visualization according to the nature of the network.

Format

• davis.dl Southern woman: (Davis, Gardner, Gardner, 1941) affiliation network 18 \times 14.

• sampson.dl Monastery novices: (Sampson, 1969) directed, multiplex, valued, longitudinal network 18 \times 18 \times 10.

• padgett.dl Florentine families: (Padgett and Ansell, 1993) undirected, multiplex network 16 \times 16 \times 2.

• padgw.dl Florentine families' attributes: table 16 \times 3.

Source

UCINET 6 for windows: Software for social network analysis.

internal function

Description

internal function

internal function

Description

internal function