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multigraph: Plot and Manipulate Multigraphs in R

Antonio Rivero Ostoic (@mplex)



To install multigraph with the R console, R IDE, or Notebook with R kernel in.

# from CRAN
install.packages("multigraph")

or

# from Github
devtools::install_github("mplex/multigraph")

When you load the package then multiplex is automatically invoked.

library("multigraph")
# Loading required package: multiplex

Multigraph: Florentine Families dataset

Padgett's Florentine Families dataset is publicly available as a Ucinet DL file format. Use function read.dl of the multiplex package to retrieve this data.


# read the Padgett Florentine Families dataset as a Ucinet DL file
# from a public repository and storage it as an object

floflies <- multiplex::read.dl(file = "http://moreno.ss.uci.edu/padgett.dat")
# or mirror
floflies <- multiplex::read.dl(file = "http://vlado.fmf.uni-lj.si/pub/networks/data/ucinet/padgett.dat")


# adjacency matrices
floflies

, , PADGM

          ACCIAIUOL ALBIZZI BARBADORI BISCHERI CASTELLAN GINORI GUADAGNI LAMBERTES MEDICI PAZZI PERUZZI PUCCI RIDOLFI SALVIATI STROZZI TORNABUON
ACCIAIUOL         0       0         0        0         0      0        0         0      1     0       0     0       0        0       0         0
ALBIZZI           0       0         0        0         0      1        1         0      1     0       0     0       0        0       0         0
BARBADORI         0       0         0        0         1      0        0         0      1     0       0     0       0        0       0         0
BISCHERI          0       0         0        0         0      0        1         0      0     0       1     0       0        0       1         0
CASTELLAN         0       0         1        0         0      0        0         0      0     0       1     0       0        0       1         0
GINORI            0       1         0        0         0      0        0         0      0     0       0     0       0        0       0         0
GUADAGNI          0       1         0        1         0      0        0         1      0     0       0     0       0        0       0         1
LAMBERTES         0       0         0        0         0      0        1         0      0     0       0     0       0        0       0         0
MEDICI            1       1         1        0         0      0        0         0      0     0       0     0       1        1       0         1
PAZZI             0       0         0        0         0      0        0         0      0     0       0     0       0        1       0         0
PERUZZI           0       0         0        1         1      0        0         0      0     0       0     0       0        0       1         0
PUCCI             0       0         0        0         0      0        0         0      0     0       0     0       0        0       0         0
RIDOLFI           0       0         0        0         0      0        0         0      1     0       0     0       0        0       1         1
SALVIATI          0       0         0        0         0      0        0         0      1     1       0     0       0        0       0         0
STROZZI           0       0         0        1         1      0        0         0      0     0       1     0       1        0       0         0
TORNABUON         0       0         0        0         0      0        1         0      1     0       0     0       1        0       0         0

, , PADGB

          ACCIAIUOL ALBIZZI BARBADORI BISCHERI CASTELLAN GINORI GUADAGNI LAMBERTES MEDICI PAZZI PERUZZI PUCCI RIDOLFI SALVIATI STROZZI TORNABUON
ACCIAIUOL         0       0         0        0         0      0        0         0      0     0       0     0       0        0       0         0
ALBIZZI           0       0         0        0         0      0        0         0      0     0       0     0       0        0       0         0
BARBADORI         0       0         0        0         1      1        0         0      1     0       1     0       0        0       0         0
BISCHERI          0       0         0        0         0      0        1         1      0     0       1     0       0        0       0         0
CASTELLAN         0       0         1        0         0      0        0         1      0     0       1     0       0        0       0         0
GINORI            0       0         1        0         0      0        0         0      1     0       0     0       0        0       0         0
GUADAGNI          0       0         0        1         0      0        0         1      0     0       0     0       0        0       0         0
LAMBERTES         0       0         0        1         1      0        1         0      0     0       1     0       0        0       0         0
MEDICI            0       0         1        0         0      1        0         0      0     1       0     0       0        1       0         1
PAZZI             0       0         0        0         0      0        0         0      1     0       0     0       0        0       0         0
PERUZZI           0       0         1        1         1      0        0         1      0     0       0     0       0        0       0         0
PUCCI             0       0         0        0         0      0        0         0      0     0       0     0       0        0       0         0
RIDOLFI           0       0         0        0         0      0        0         0      0     0       0     0       0        0       0         0
SALVIATI          0       0         0        0         0      0        0         0      1     0       0     0       0        0       0         0
STROZZI           0       0         0        0         0      0        0         0      0     0       0     0       0        0       0         0
TORNABUON         0       0         0        0         0      0        0         0      1     0       0     0       0        0       0         0

Object floflies represents the Florentine families network where "PADGM" are marriage relations and "PADGB" correspond to business ties among the 16 actors.


Plotting multigraphs

Graph of the Florentine families network using multigraph function with the default circular layout:

multigraph(floflies)

Default layout of multigraph


Check also out the vector image of this multigraph, and note that with vector graphics the rendering may vary according to the device used.


Force-directed layout

Besides a circular layout, another possibility is to apply a force-directed layout for the visualization of the multiplex network. Function multigraph provides a number of arguments for graph, edges, and nodes levels, which can be recorded in an object list named scp to be used in the scope argument of the function.


# define scope of node / edge / graph characteristics as list object
scp <- list(directed = FALSE, cex = 6, fsize = 7, pos = 0, vcol = 8, ecol = 1, lwd = 2, bwd = .5)

# plot graph with customized format
multigraph(floflies, layout = "force", seed = 2, scope = scp)

Force directed layout of multigraph vector image



# plot graph with customized format
multigraph(floflies, layout = "force", seed = 2, scope = scp, lty = 2:1, pch = 13)

Force directed layout of multigraph different shapes vector image


Note that when the graph is depicted as undirected, then the reciprocal ties by default are collapsed. You can prevent this to happen by setting the argument collRecip to FALSE. Some arguments such as cex, lwd, lty, pch are graphical parameters of the graphics package to set the shape of both the vertices and the edges. Other arguments like bwd to specify the width of the bundle type, fsize for the size of the font used in node labels, or ecol and vcol for the color of respectively edges and vertices are complementary in multigraph. Moreover, by setting the pos argument to 0, the actor labels are placed in the middle of the nodes.



Multigraphs with Actor Attributes

Some actor attributes of the Florentine Families network.

flofliesatt <- multiplex::read.dl(file = "http://moreno.ss.uci.edu/padgw.dat")
# or mirror
flofliesatt <- multiplex::read.dl(file = "http://vlado.fmf.uni-lj.si/pub/networks/data/ucinet/padgw.dat")

Look at flofliesatt that storages attribute information

flofliesatt

          WEALTH #PRIORS #TIES
ACCIAIUOL     10      53     2
ALBIZZI       36      65     3
RIDOLFI       27      38     4
STROZZI      146      74    29
BARBADORI     55       0    14
BISCHERI      44      12     9
CASTELLAN     20      22    18
GUADAGNI       8      21    14
LAMBERTES     42       0    14
MEDICI       103      53    54
PAZZI         48       0     7
PERUZZI       49      42    32
SALVIATI      10      35     5
TORNABUON     48       0     7
GINORI        32       0     9
PUCCI          3       0     1

However, in order to depict the multigraph of floflies with the information contained in flofliesatt, be sure that the order of the actors matches in both objects.

flofliesatt <- flofliesatt[order(rownames(flofliesatt)), ]

flofliesatt

          WEALTH #PRIORS #TIES
ACCIAIUOL     10      53     2
ALBIZZI       36      65     3
BARBADORI     55       0    14
BISCHERI      44      12     9
CASTELLAN     20      22    18
GINORI        32       0     9
GUADAGNI       8      21    14
LAMBERTES     42       0    14
MEDICI       103      53    54
PAZZI         48       0     7
PERUZZI       49      42    32
PUCCI          3       0     1
RIDOLFI       27      38     4
SALVIATI      10      35     5
STROZZI      146      74    29
TORNABUON     48       0     7

Now flofliesatt matches floflies for the plotting.



Redefine the scope in scp to depict this network in a way that the size of the vertices reflects the wealth of the actors.

# redefine scope of node / edge / graph characteristics 
scp <- list(directed = FALSE, fsize = 8, pos = 0, lwd = 2, ecol = 1, vcol = 5)

# plot graph with customized format and actor attributes
multigraph(floflies, layout = "force", seed = 1, scope = scp, cex = flofliesatt[,1])

Force directed layout layout of multigraph with attributes vector image


The clu argument serves to establish the clustering of the network with three classes of actors differentiated by the colors of the vertices.

# define scope of node / edge / graph characteristics 
scp2 <- list(directed = FALSE, fsize = 8, pos = 0, lwd = 2, ecol = "white", 
+  vcol = c("orange","blue","white"), clu = c(1,1,1,2,2,1,2,2,1,1,2,3,1,1,2,1), alpha = c(.5, 1, .2))

# plot graph with customized format and actor attributes
multigraph(floflies, layout = "force", seed = 1, scope = scp2, cex = flofliesatt[,1], bg = 1)

Force directed layout of multigraph with clustering vector image

As a result, there are different ways to set the colors, and the alpha vector argument serves to set the transparency of colors in vertices, edges, and the graph background.




Bipartite Graph: Southern Women dataset

Support for the visualization of two-mode networks is also given by multigraph, and for the Southern Women classic dataset to illustrate some of the layout options with this package.

# read the Ucinet DL file of Davis, Gardner, Gardner Southern Women
# dataset from a public repository and storage it as an object

swomen <- multiplex::read.dl(file = "http://moreno.ss.uci.edu/davis.dat")
# or mirror
swomen <- multiplex::read.dl(file = "http://vlado.fmf.uni-lj.si/pub/networks/data/ucinet/davis.dat")


### take a look
swomen

          E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14
EVELYN     1  1  1  1  1  1  0  1  1   0   0   0   0   0
LAURA      1  1  1  0  1  1  1  1  0   0   0   0   0   0
THERESA    0  1  1  1  1  1  1  1  1   0   0   0   0   0
BRENDA     1  0  1  1  1  1  1  1  0   0   0   0   0   0
CHARLOTTE  0  0  1  1  1  0  1  0  0   0   0   0   0   0
FRANCES    0  0  1  0  1  1  0  1  0   0   0   0   0   0
ELEANOR    0  0  0  0  1  1  1  1  0   0   0   0   0   0
PEARL      0  0  0  0  0  1  0  1  1   0   0   0   0   0
RUTH       0  0  0  0  1  0  1  1  1   0   0   0   0   0
VERNE      0  0  0  0  0  0  1  1  1   0   0   1   0   0
MYRA       0  0  0  0  0  0  0  1  1   1   0   1   0   0
KATHERINE  0  0  0  0  0  0  0  1  1   1   0   1   1   1
SYLVIA     0  0  0  0  0  0  1  1  1   1   0   1   1   1
NORA       0  0  0  0  0  1  1  0  1   1   1   1   1   1
HELEN      0  0  0  0  0  0  1  1  0   1   1   1   1   1
DOROTHY    0  0  0  0  0  0  0  1  1   1   0   1   0   0
OLIVIA     0  0  0  0  0  0  0  0  1   0   1   0   0   0
FLORA      0  0  0  0  0  0  0  0  1   0   1   0   0   0

In this case, the information can be contained in a data frame or an array as before.


Plotting two-mode data

Function bmgraph serves to plot two-mode data or an affiliation network as a bipartite graph.

bmgraph(swomen)

Default layout of bmgraph vector image

In this case, actor and events have different shape by default.


Similarly to multigraph the color and shape of edges and vertices can be modified by equal arguments, and we can mirror the X axis of the plot.

# define scope of node / edge / graph characteristics as list object
scp3 <- list(cex = 3, fsize = 8, pch = c(19, 15), lwd = 1.5, vcol = 2:3, fsize = 7)

# Plot bipartite graph with customized format and horizontal reflection
bmgraph(swomen, scope = scp3, mirrorX = TRUE)

Mirror X of bmgraph vector image


Option bip3 splits the actors in two columns, whereas bip3e will split the events.

bmgraph(swomen, layout = "bip3", scope = scp3)

Mirror X of bmgraph vector image


Bipartite graph with clustering information of Southern Women network as in Batagelj et al, 2014 (p. 29).

# clustering of network members for permutation 
clup <- list(c(8,9,7,6,1,4,2,3,5,17,18,13,16,11,10,15,14,12),
        c(5,1,4,2,3,9,8,7,6,11,12,10,13,14))

# clustering of network members for layout 
clunm <- list(c(rep(1,9),rep(2,9)),c(rep(1,5),rep(2,4),rep(3,5)))

# bipartite graph with clustering
bmgraph(swomen, layout = "bipc", scope = scp3, clu = clunm, perm = clup)

clustering bmgraph vector image


The binomial projection of a two-mode dataset allows obtaining a force directed layout that in this case the image is clockwise rotated 65 degrees.

bmgraph(swomen, layout = "force", seed = 1, scope = scp3, rot = 65)

Force directed layout of bmgraph vector image



Function bmgraph stands for a bipartite multigraph because the actors can be affiliated by different means.

bmgraph(floflies, ecol = 1)

bipartite graph of floflies vector image



Cayley graph

See Plot partially ordered semigroup

or

?ccgraph


Multilevel graph

See Multilevel Structure of G20 Trade Network

or

?mlgraph


Notice for R (>4.0.0), use multiplex version 3 or higher.