Clustering with the Leiden Algorithm on Multiplex Graphs
The Leiden R package supports calling built-in methods for Multiplex graphs. This vignette assumes you already have the ‘leiden’ package installed. See the other vignettes for details.
Set up
First we import the functions required in the package.
library("leiden")
We also require a example multiplex graph. Here we import a dataset from the ‘mplex’ package (bear in mind this is a remote package not available on CRAN).
remotes::install_github("Achab94/mplex")
multiplex_graph <- mplex::aarhus_mplex
multiplex_graph
#> $lunch
#> IGRAPH 2059d07 DN-- 61 193 --
#> + attr: name (v/c)
#> + edges from 2059d07 (vertex names):
#> [1] U102->U139 U102->U33 U22 ->U26 U22 ->U41 U22 ->U42 U22 ->U49 U26 ->U41 U26 ->U42 U26 ->U49 U29 ->U32
#> [11] U29 ->U17 U29 ->U14 U32 ->U17 U32 ->U130 U32 ->U14 U32 ->U73 U41 ->U42 U42 ->U49 U42 ->U47 U59 ->U91
#> [21] U59 ->U126 U59 ->U110 U59 ->U53 U59 ->U65 U59 ->U67 U59 ->U72 U97 ->U71 U97 ->U126 U97 ->U37 U97 ->U4
#> [31] U97 ->U69 U97 ->U6 U124->U109 U124->U126 U124->U47 U124->U99 U17 ->U14 U17 ->U23 U17 ->U73 U71 ->U4
#> [41] U71 ->U67 U71 ->U63 U86 ->U130 U91 ->U126 U91 ->U110 U91 ->U53 U91 ->U65 U91 ->U67 U91 ->U72 U109->U126
#> [51] U109->U134 U109->U18 U109->U3 U109->U47 U109->U54 U109->U62 U109->U76 U109->U79 U109->U90 U109->U99
#> [61] U126->U54 U126->U90 U126->U37 U126->U110 U126->U113 U126->U138 U126->U72 U126->U69 U126->U6 U130->U134
#> [71] U130->U79 U130->U4 U130->U110 U134->U54 U134->U62 U134->U76 U134->U79 U134->U90 U134->U99 U134->U13
#> + ... omitted several edges
#>
#> $facebook
#> IGRAPH f219f59 DN-- 61 127 --
#> + attr: name (v/c)
#> + edges from f219f59 (vertex names):
#> [1] U29 ->U32 U29 ->U91 U32 ->U71 U32 ->U91 U32 ->U130 U32 ->U4 U32 ->U110 U32 ->U67 U42 ->U49 U42 ->U79
#> [11] U42 ->U142 U59 ->U91 U59 ->U110 U59 ->U113 U59 ->U67 U124->U91 U124->U109 U124->U130 U124->U134 U124->U18
#> [21] U124->U3 U124->U47 U124->U54 U124->U76 U124->U79 U124->U69 U124->U6 U71 ->U79 U71 ->U4 U71 ->U110
#> [31] U71 ->U67 U91 ->U79 U91 ->U10 U91 ->U142 U91 ->U4 U91 ->U110 U91 ->U113 U91 ->U65 U91 ->U67 U91 ->U69
#> [41] U109->U18 U109->U47 U109->U54 U109->U76 U109->U79 U130->U134 U130->U18 U130->U3 U130->U47 U130->U76
#> [51] U130->U79 U130->U142 U130->U4 U130->U67 U18 ->U3 U18 ->U47 U18 ->U54 U18 ->U76 U18 ->U79 U3 ->U47
#> [61] U3 ->U54 U3 ->U76 U3 ->U79 U47 ->U54 U47 ->U76 U47 ->U79 U47 ->U142 U47 ->U4 U54 ->U76 U54 ->U79
#> [71] U54 ->U10 U54 ->U142 U54 ->U4 U76 ->U79 U76 ->U4 U76 ->U112 U79 ->U142 U79 ->U110 U79 ->U65 U10 ->U142
#> + ... omitted several edges
#>
#> $coauthor
#> IGRAPH 8b7e975 D--- 61 27 --
#> + edges from 8b7e975:
#> [1] 10->11 12->13 18->46 23->46 23->49 23->52 26->27 26->28 26->30 26->33 26->36 28->33 30->36 38->54 39->55 4-> 6
#> [17] 46->48 46->49 49->52 6->14 8->37 56->56 57->57 58->58 59->59 60->60 61->61
#>
#> $leisure
#> IGRAPH 500ba7c DN-- 61 88 --
#> + attr: name (v/c)
#> + edges from 500ba7c (vertex names):
#> [1] U22 ->U42 U29 ->U32 U29 ->U126 U42 ->U49 U42 ->U79 U42 ->U142 U59 ->U91 U59 ->U110 U59 ->U65 U59 ->U72
#> [11] U124->U91 U124->U126 U124->U18 U124->U99 U17 ->U91 U17 ->U14 U17 ->U23 U17 ->U73 U91 ->U126 U91 ->U54
#> [21] U91 ->U90 U91 ->U110 U91 ->U113 U91 ->U138 U91 ->U53 U91 ->U65 U91 ->U72 U91 ->U69 U109->U126 U109->U54
#> [31] U109->U76 U109->U90 U126->U54 U126->U90 U126->U110 U126->U69 U18 ->U62 U18 ->U76 U18 ->U99 U3 ->U54
#> [41] U3 ->U90 U47 ->U76 U54 ->U76 U54 ->U79 U54 ->U90 U54 ->U10 U62 ->U76 U76 ->U79 U76 ->U90 U79 ->U90
#> [51] U79 ->U99 U79 ->U73 U79 ->U65 U90 ->U6 U10 ->U13 U10 ->U142 U10 ->U37 U10 ->U73 U142->U37 U142->U68
#> [61] U106->U41 U106->U118 U14 ->U19 U14 ->U23 U14 ->U73 U19 ->U23 U19 ->U73 U23 ->U73 U4 ->U67 U110->U113
#> [71] U110->U138 U110->U65 U110->U67 U113->U138 U113->U65 U138->U72 U107->U32 U107->U17 U107->U91 U65 ->U72
#> + ... omitted several edges
#>
#> $work
#> IGRAPH 3351fca DN-- 61 194 --
#> + attr: name (v/c)
#> + edges from 3351fca (vertex names):
#> [1] U22 ->U26 U22 ->U41 U22 ->U42 U22 ->U49 U26 ->U32 U26 ->U42 U26 ->U49 U26 ->U97 U26 ->U71 U26 ->U130
#> [11] U26 ->U79 U26 ->U110 U26 ->U140 U29 ->U32 U29 ->U17 U32 ->U97 U32 ->U17 U32 ->U86 U32 ->U130 U32 ->U14
#> [21] U32 ->U73 U32 ->U110 U42 ->U79 U59 ->U91 U59 ->U110 U59 ->U67 U97 ->U71 U97 ->U4 U97 ->U67 U124->U130
#> [31] U124->U4 U139->U26 U139->U29 U139->U97 U139->U71 U139->U10 U139->U14 U139->U19 U139->U107 U139->U67
#> [41] U139->U123 U139->U1 U17 ->U14 U17 ->U23 U17 ->U73 U71 ->U14 U71 ->U19 U71 ->U4 U71 ->U110 U71 ->U67
#> [51] U71 ->U63 U71 ->U6 U71 ->U140 U91 ->U110 U91 ->U113 U91 ->U138 U91 ->U53 U91 ->U65 U91 ->U67 U91 ->U72
#> [61] U109->U130 U109->U54 U109->U62 U126->U110 U126->U67 U126->U69 U130->U134 U130->U18 U130->U47 U130->U54
#> [71] U130->U62 U130->U76 U130->U79 U130->U99 U130->U10 U130->U4 U134->U99 U134->U4 U18 ->U62 U3 ->U90
#> + ... omitted several edges
Usage
Multiplex graph objects
Now we have a multiplex graph structure. This multiplex graph is a list of different igraph object, in the case representing different relationships between the sample people.
names(multiplex_graph)
#> [1] "lunch" "facebook" "coauthor" "leisure" "work"
Here we import a plotting function to display these 5 groups.
library("graphsim")
library("RColorBrewer")
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$lunch, main = "lunch", col.arrow = brewer.pal(5, "Pastel1")[1], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$work, main = "work", col.arrow = brewer.pal(5, "Pastel1")[2], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$facebook, main = "facebook", col.arrow = brewer.pal(5, "Pastel1")[3], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$leisure, main = "leisure", col.arrow = brewer.pal(5, "Pastel1")[4], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$coauthor, main = "coauthor", col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
This data can also be represented by an adjacency matrix derived from a graph object.
library("igraph")
multiplex_matrix <- lapply(multiplex_graph, igraph::as_adjacency_matrix)
multiplex_matrix
#> $lunch
#> 61 x 61 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 61 column names 'U102', 'U139', 'U33' ... ]]
#>
#> U102 . 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U139 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U33 . . . . . . 1 . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 . . . . . 1
#> U106 . . . . . 1 . . . 1 1 . . 1 1 1 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U107 . . . . . . . . . . . 1 1 . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U118 . . . . . . . . . 1 1 . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U123 . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . 1 . . . . . . . . . 1 . . . . . . 1 . . . . . 1
#> U1 . . . . . . . . . . . 1 1 . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 1 1 . . 1 . . . . . . . . . . . .
#> U21 . . . . . . . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . . . . . . . . . 1 . . . . . . . 1 . . . . 1 .
#> U22 . . . . . . . . . . 1 . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U26 . . . . . . . . . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U29 . . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . .
#> U32 . . . . . . . . . . . . . . . . . . . 1 . . . . . 1 . . . . . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . .
#> U41 . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U42 . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U59 . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . . . . . . . . . . . . . . . . . . . 1 . . 1 1 1 1 . . . . .
#> U97 . . . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . . . . . . . . . . . . . . 1 1 . . . . . . . . . . . 1 .
#> U124 . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . 1 . . . . . 1 . . . . . . . . . . . . . . . . . . . . .
#> U17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . 1 . . . . . . . . . . . .
#> U71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 . . . . . 1
#> U86 . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U91 . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1 . . 1 1 1 1 . . . . .
#> U109 . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 1 1 1 1 1 1 1 1 1 . . . . . . . . . . . . . . . . . . . . .
#> U126 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . . . . 1 . . 1 1 1 . . . 1 . . . 1 .
#> U130 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . 1 . 1 . . . . . . . . . . .
#> U134 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 . 1 . . . . . 1 . . . . . . . . . 1 . . .
#> U18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 1 1 1 1 1 . . . . . . . . . . . . . . . . . . . . .
#> U3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 . . . . . . . . . . . . . . . . . . . . . .
#> U47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . . . . . . . . . . . . . . . . . . . .
#> U54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 . . . . . . . . . . . . . . . . . . . . . .
#> U62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . .
#> U76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . .
#> U79 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . . . . . . . . . . . . . . 1
#> U90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . . . . . . . . . .
#> U13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . . .
#> U142 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . .
#> U14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . 1 . . . . . . . . . . . .
#> U19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . . .
#> U23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . .
#> U37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 .
#> U4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 1 1 . 1
#> U73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U110 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . 1 . . . . .
#> U113 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 1 . . . . .
#> U138 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . .
#> U53 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . . . .
#> U65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . .
#> U67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1
#> U72 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 .
#> U112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . .
#> U48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . .
#> U68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#>
#> U102 . . . .
#> U139 . . . .
#> U33 . . . .
#> U106 . . . .
#> U107 . . . .
#> U118 . . . .
#> U123 . . . .
#> U1 . . . .
#> U21 1 . . .
#> U22 . . . .
#> U26 . . . .
#> U29 . . . .
#> U32 . . . .
#> U41 . . . .
#> U42 . . . .
#> U49 . . . .
#> U59 . . . .
#> U97 1 . . .
#> U124 . . . .
#> U17 . . . .
#> U71 . . . .
#> U86 . . . .
#> U91 . . . .
#> U109 . . . .
#> U126 1 . . .
#> U130 . . . .
#> U134 . 1 . .
#> U18 . . . .
#> U3 . . . .
#> U47 . . . .
#> U54 . . . .
#> U62 . . . .
#> U76 . . . .
#> U79 . . . .
#> U90 1 . . .
#> U99 . . . .
#> U10 . . . .
#> U13 . . . .
#> U142 . . . .
#> U14 . . . .
#> U19 . . . .
#> U23 . . . .
#> U37 1 . . .
#> U4 . 1 . 1
#> U73 . . . .
#> U110 . . . .
#> U113 . . . .
#> U138 . . . .
#> U53 . . . .
#> U65 . . . .
#> U67 . . . .
#> U72 . . . .
#> U112 . . . .
#> U48 . 1 . 1
#> U68 . 1 . 1
#> U69 1 . . .
#> U63 . . . .
#> U6 . . . .
#> U92 . . . 1
#> U140 . . . .
#> U141 . . . .
#>
#> $facebook
#> 61 x 61 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 61 column names 'U102', 'U139', 'U33' ... ]]
#>
#> U102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U139 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U106 . . . . 1 . 1 1 1 . . 1 1 . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U107 . . . . . . . . . . . 1 1 . . . . . 1 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U118 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U123 . . . . . . . . . . . . 1 . 1 1 . . . . 1 . 1 . . 1 . . . 1 . . . . . . . . 1 . . . . 1 . . . . . . 1 . . . . . .
#> U1 . . . . . . . . . . . 1 1 . . . . . . . 1 . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . . . . . . . . . . .
#> U21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 .
#> U22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U29 . . . . . . . . . . . . 1 . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U32 . . . . . . . . . . . . . . . . . . . . 1 . 1 . . 1 . . . . . . . . . . . . . . . . . 1 . 1 . . . . 1 . . . . . .
#> U41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U42 . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . . . . . . . .
#> U49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U59 . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . 1 . . . . . .
#> U97 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U124 . . . . . . . . . . . . . . . . . . . . . . 1 1 . 1 1 1 1 1 1 . 1 1 . . . . . . . . . . . . . . . . . . . . . 1 .
#> U17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . 1 . 1 . . . . 1 . . . . . .
#> U86 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U91 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . 1 . . . . 1 . 1 1 . . 1 1 . . . . 1 .
#> U109 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 1 . 1 1 . . . . . . . . . . . . . . . . . . . . . . .
#> U126 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U130 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 . . 1 1 . . . . 1 . . . . 1 . . . . . . 1 . . . . . .
#> U134 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . 1 1 . . . . . . . . . . . . . . . . . . . . . . .
#> U3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . 1 1 . . . . . . . . . . . . . . . . . . . . . . .
#> U47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 1 . . . . 1 . . . . 1 . . . . . . . . . . . . .
#> U54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . 1 . 1 . . . . 1 . . . . . . . . . . . . .
#> U62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . 1 . . . . . . . . 1 . . . .
#> U79 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 . . . 1 . . . . . . .
#> U90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . . .
#> U13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U142 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . . . 1 . . . . . .
#> U14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . . .
#> U73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U110 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . . .
#> U113 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . 1 .
#> U138 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U53 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . .
#> U67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 .
#> U72 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#>
#> U102 . . . .
#> U139 . . . .
#> U33 . . . .
#> U106 . . . .
#> U107 . . . .
#> U118 . . . .
#> U123 . . . .
#> U1 . . . .
#> U21 1 . . .
#> U22 . . . .
#> U26 . . . .
#> U29 . . . .
#> U32 . . . .
#> U41 . . . .
#> U42 . . . .
#> U49 . . . .
#> U59 . . . .
#> U97 . . . .
#> U124 1 . . .
#> U17 . . . .
#> U71 . . . .
#> U86 . . . .
#> U91 . . . .
#> U109 . . . .
#> U126 . . . .
#> U130 . . . .
#> U134 . . . .
#> U18 . . . .
#> U3 . . . .
#> U47 . . . .
#> U54 . . . .
#> U62 . . . .
#> U76 . . . .
#> U79 . . . .
#> U90 . . . .
#> U99 . . . .
#> U10 . . . .
#> U13 . . . .
#> U142 . . . .
#> U14 . . . .
#> U19 . . . .
#> U23 . . . .
#> U37 . . . .
#> U4 . . . .
#> U73 . . . .
#> U110 . . . .
#> U113 . . . .
#> U138 . . . .
#> U53 . . . .
#> U65 . . . .
#> U67 1 . . .
#> U72 . . . .
#> U112 . . . .
#> U48 . . . .
#> U68 . . . .
#> U69 1 . . .
#> U63 . . . .
#> U6 . . . .
#> U92 . 1 . .
#> U140 . . 1 .
#> U141 . . . 1
#>
#> $coauthor
#> 61 x 61 sparse Matrix of class "dgCMatrix"
#>
#> [1,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [2,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [3,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [4,] . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [5,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [6,] . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [7,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [8,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . .
#> [9,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [10,] . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [11,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [12,] . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [13,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [14,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [15,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [16,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [17,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [18,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . .
#> [19,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [20,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [21,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [22,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [23,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . . 1 . . . . .
#> [24,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [25,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [26,] . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . 1 . . 1 . . 1 . . . . . . . . . . . . . . . . . . . . .
#> [27,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [28,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
#> [29,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [30,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . .
#> [31,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [32,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [33,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [34,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [35,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [36,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [37,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [38,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . .
#> [39,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . .
#> [40,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [41,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [42,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [43,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [44,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [45,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [46,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . .
#> [47,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [48,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [49,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . .
#> [50,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [51,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [52,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [53,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [54,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [55,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [56,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 .
#> [57,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
#> [58,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [59,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [60,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [61,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#>
#> [1,] . . . .
#> [2,] . . . .
#> [3,] . . . .
#> [4,] . . . .
#> [5,] . . . .
#> [6,] . . . .
#> [7,] . . . .
#> [8,] . . . .
#> [9,] . . . .
#> [10,] . . . .
#> [11,] . . . .
#> [12,] . . . .
#> [13,] . . . .
#> [14,] . . . .
#> [15,] . . . .
#> [16,] . . . .
#> [17,] . . . .
#> [18,] . . . .
#> [19,] . . . .
#> [20,] . . . .
#> [21,] . . . .
#> [22,] . . . .
#> [23,] . . . .
#> [24,] . . . .
#> [25,] . . . .
#> [26,] . . . .
#> [27,] . . . .
#> [28,] . . . .
#> [29,] . . . .
#> [30,] . . . .
#> [31,] . . . .
#> [32,] . . . .
#> [33,] . . . .
#> [34,] . . . .
#> [35,] . . . .
#> [36,] . . . .
#> [37,] . . . .
#> [38,] . . . .
#> [39,] . . . .
#> [40,] . . . .
#> [41,] . . . .
#> [42,] . . . .
#> [43,] . . . .
#> [44,] . . . .
#> [45,] . . . .
#> [46,] . . . .
#> [47,] . . . .
#> [48,] . . . .
#> [49,] . . . .
#> [50,] . . . .
#> [51,] . . . .
#> [52,] . . . .
#> [53,] . . . .
#> [54,] . . . .
#> [55,] . . . .
#> [56,] . . . .
#> [57,] . . . .
#> [58,] 1 . . .
#> [59,] . 1 . .
#> [60,] . . 1 .
#> [61,] . . . 1
#>
#> $leisure
#> 61 x 61 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 61 column names 'U102', 'U139', 'U33' ... ]]
#>
#> U102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U139 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U106 . . . . . 1 . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U107 . . . . . . . . . . . . 1 . . . . . . 1 . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U118 . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U123 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U1 . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . 1 . . 1 . . . . . . . . . . . .
#> U21 . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U22 . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U29 . . . . . . . . . . . . 1 . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U42 . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . . . . . . . .
#> U49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U59 . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 . 1 . . . . .
#> U97 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U124 . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . 1 . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . .
#> U17 . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . 1 . 1 . . 1 . . . . . . . . . . . .
#> U71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U86 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U91 . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . 1 . . . 1 . . . . . . . . . . 1 1 1 1 1 . 1 . . . 1 .
#> U109 . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . 1 . 1 . 1 . . . . . . . . . . . . . . . . . . . . . .
#> U126 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . . . . . . . 1 . . . . . . . . . 1 .
#> U130 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U134 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . 1 . . . . . . . . . . . . . . . . . . . . .
#> U3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . . . . . . . . . . . . . . . . . . .
#> U47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
#> U54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . 1 . . . . . . . . . . . . . . . . . . . .
#> U62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
#> U76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . . . . . . . . . . . . . . . .
#> U79 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . . . . . 1 . . . . 1 . . . . . . .
#> U90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . 1 . 1 . . . . . . . . . . . .
#> U13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U142 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . 1 . .
#> U14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . 1 . . . . . . . . . . . .
#> U19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . . .
#> U23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . .
#> U37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . .
#> U73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U110 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . 1 1 . . . . . .
#> U113 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . . . . . .
#> U138 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . .
#> U53 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . .
#> U67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U72 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#>
#> U102 . . . .
#> U139 . . . .
#> U33 . . . .
#> U106 . . . .
#> U107 . . . .
#> U118 . . . .
#> U123 . . . .
#> U1 . . . .
#> U21 . . . .
#> U22 . . . .
#> U26 . . . .
#> U29 . . . .
#> U32 . . . .
#> U41 . . . .
#> U42 . . . .
#> U49 . . . .
#> U59 . . . .
#> U97 . . . .
#> U124 . . . .
#> U17 . . . .
#> U71 . . . .
#> U86 . . . .
#> U91 . . . .
#> U109 . . . .
#> U126 . . . .
#> U130 . . . .
#> U134 . . . .
#> U18 . . . .
#> U3 . . . .
#> U47 . . . .
#> U54 . . . .
#> U62 . . . .
#> U76 . . . .
#> U79 . . . .
#> U90 1 . . .
#> U99 . . . .
#> U10 . . . .
#> U13 . . . .
#> U142 . . . .
#> U14 . . . .
#> U19 . . . .
#> U23 . . . .
#> U37 . . . .
#> U4 . . . .
#> U73 . . . .
#> U110 . . . .
#> U113 . . . .
#> U138 . . . .
#> U53 . . . .
#> U65 . . . .
#> U67 . . . .
#> U72 . . . .
#> U112 . . . .
#> U48 . . . .
#> U68 . . . 1
#> U69 . . . .
#> U63 . . . .
#> U6 . . . .
#> U92 . . . .
#> U140 . . . .
#> U141 . . . .
#>
#> $work
#> 61 x 61 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 61 column names 'U102', 'U139', 'U33' ... ]]
#>
#> U102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U139 . . . . 1 . 1 1 . . 1 1 . . . . . 1 . . 1 . . . . . . . . . . . . . . . 1 . . 1 1 . . . . . . . . . 1 . . . . . .
#> U33 . . . . . 1 1 . 1 . 1 . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . . . 1 . . . . . 1
#> U106 . . . . . 1 1 . . . 1 . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U107 . . . . . . . . . . . 1 1 . . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U118 . . . . . . 1 . . . 1 . . 1 . . . 1 . . 1 . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . 1 . . . . . .
#> U123 . . . . . . . . . 1 1 . . . 1 1 . 1 1 1 1 . . . . 1 . 1 1 1 1 1 1 1 1 1 . . 1 . . . . 1 . 1 . . . . 1 . . . . . 1
#> U1 . . . . . . . . . . 1 . 1 . . . . . 1 . 1 . . . . 1 . . . . . . . 1 . . 1 . . 1 1 1 . . 1 . . . . . . . . . . . .
#> U21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . .
#> U22 . . . . . . . . . . 1 . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U26 . . . . . . . . . . . . 1 . 1 1 . 1 . . 1 . . . . 1 . . . . . . . 1 . . . . . . . . . . . 1 . . . . . . . . . . .
#> U29 . . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U32 . . . . . . . . . . . . . . . . . 1 . 1 . 1 . . . 1 . . . . . . . . . . . . . 1 . . . . 1 1 . . . . . . . . . . .
#> U41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U42 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . .
#> U49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U59 . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . . .
#> U97 . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . 1 . . . . . .
#> U124 . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . .
#> U17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . 1 . . . . . . . . . . . .
#> U71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . 1 . 1 . . . . 1 . . . . . 1
#> U86 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U91 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 . . . . .
#> U109 . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 1 . . . . . . . . . . . . . . . . . . . . . . . . .
#> U126 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . 1 .
#> U130 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . 1 1 1 1 1 . 1 1 . . . . . . 1 . . . . . . . . . . . . .
#> U134 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 1 . . . . . . . . . . . . .
#> U18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . .
#> U3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . .
#> U47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . . . . . . . . . . . . . . . . . .
#> U54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . 1 . . 1 . . 1 . . . . . . . . . . . . .
#> U62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
#> U76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . .
#> U79 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . 1 . 1 . . . . . . . . . . .
#> U90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . .
#> U99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . .
#> U10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . . 1 . . . . . . . . . . . .
#> U13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . 1 . . .
#> U142 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . 1 . .
#> U14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . 1 . . . . . . . . . . . .
#> U19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . . .
#> U23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . .
#> U37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . .
#> U4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 1 1 . 1
#> U73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U110 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . 1 1 . . . . .
#> U113 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . . . . . .
#> U138 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . .
#> U53 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 . . . . .
#> U67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 1
#> U72 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . .
#> U48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 .
#> U68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> U141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#>
#> U102 . . . .
#> U139 . . . .
#> U33 . . . .
#> U106 . . . .
#> U107 . . . .
#> U118 . . . .
#> U123 . . . .
#> U1 . . . .
#> U21 . . . .
#> U22 . . . .
#> U26 . . 1 .
#> U29 . . . .
#> U32 . . . .
#> U41 . . . .
#> U42 . . . .
#> U49 . . . .
#> U59 . . . .
#> U97 . . . .
#> U124 . . . .
#> U17 . . . .
#> U71 1 . 1 .
#> U86 . . . .
#> U91 . . . .
#> U109 . . . .
#> U126 . . . .
#> U130 . . . .
#> U134 . . . .
#> U18 . . . .
#> U3 . . . .
#> U47 . . . .
#> U54 . . . .
#> U62 . . . .
#> U76 . . . .
#> U79 . . . .
#> U90 . . . .
#> U99 . . . .
#> U10 . . . .
#> U13 . 1 . .
#> U142 . . . .
#> U14 . . . .
#> U19 . . . .
#> U23 . . . .
#> U37 . . . .
#> U4 . 1 . 1
#> U73 . . . .
#> U110 . . . .
#> U113 . . . .
#> U138 . . . .
#> U53 . . . .
#> U65 . . . .
#> U67 1 . . .
#> U72 . . . .
#> U112 . . . .
#> U48 . . . .
#> U68 . . . 1
#> U69 . . . .
#> U63 . . . .
#> U6 . . . .
#> U92 . . . .
#> U140 . . . .
#> U141 . . . .
Running the Leiden algorithm in R
Then the Leiden algorithm can be run on the adjacency matrix using a partition type for Multiplex graphs. Here the types are computed automatically.
partition <- leiden(multiplex_graph,
partition_type = "CPMVertexPartition",
resolution_parameter = 0.025,
seed = 9001)
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
table(partition)
#> partition
#> 1 2 3 4 5
#> 34 12 8 6 1
Here we can see that the partitions are defined across all graphs in the list.
library("graphsim")
library("RColorBrewer")
node.cols <- brewer.pal(min(c(9, partition)),"Pastel1")[partition]
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$lunch, main = "lunch", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[1], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$work, main = "work", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[2], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$facebook, main = "facebook", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[3], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$leisure, main = "leisure", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[4], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
This can also be run on a list of adjacency matrices giving the same results.
partition <- leiden(multiplex_matrix,
partition_type = "CPMVertexPartition",
resolution_parameter = 0.025,
seed = 9001)
#> Warning in deparse(substitute(arg)): NAs introduced by coercion to integer range
#> Warning in paste(sig, collapse = "#"): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in deparse(substitute(arg)): NAs introduced by coercion to integer range
#> Warning in paste(sig, collapse = "#"): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in deparse(substitute(arg)): NAs introduced by coercion to integer range
#> Warning in paste(sig, collapse = "#"): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in deparse(substitute(arg)): NAs introduced by coercion to integer range
#> Warning in paste(sig, collapse = "#"): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in deparse(substitute(arg)): NAs introduced by coercion to integer range
#> Warning in paste(sig, collapse = "#"): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in deparse(x[[1L]]): NAs introduced by coercion to integer range
#> Warning in deparse(expr, width.cutoff, ...): NAs introduced by coercion to integer range
#> Warning in paste(deparse(expr, width.cutoff, ...), collapse = collapse): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in paste0("igraph::", x): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
table(partition)
#> partition
#> 1 2 3 4 5
#> 34 12 8 6 1
Fine-tuning with resolution
The resolution parameter applies on multiplex graphs to fine-tuning how many clusters are detected.
partition <- leiden(multiplex_graph, partition_type = "CPMVertexPartition", resolution_parameter = 0.1, seed = 42)
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
table(partition)
#> partition
#> 1 2 3 4 5 6 7 8 9 10
#> 14 11 11 8 7 4 3 1 1 1
library("graphsim")
library("RColorBrewer")
node.cols <- brewer.pal(min(c(9, partition)),"Pastel1")[partition]
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$lunch, main = "lunch", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[1], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$work, main = "work", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[2], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$facebook, main = "facebook", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[3], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$leisure, main = "leisure", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[4], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
Fine-tuning with maximum community size
The resolutionmax_comm_size` parameter applies on multiplex graphs to fine-tuning the size of clusters detected.
partition <- leiden(multiplex_graph, partition_type = "CPMVertexPartition", max_comm_size = 8, resolution_parameter = 0.1, seed = 42)
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
table(partition)
#> partition
#> 1 2 3 4 5 6 7 8 9 10 11 12
#> 8 8 8 7 7 6 5 5 4 1 1 1
library("graphsim")
library("RColorBrewer")
node.cols <- brewer.pal(min(c(9, partition)),"Pastel1")[partition]
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$lunch, main = "lunch", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[1], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$work, main = "work", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[2], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$facebook, main = "facebook", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[3], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$leisure, main = "leisure", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[4], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
Multiplex cost functions
Any defined cost function is supported for multiplex graphs. For example, the Modularity Vertex Partition is also supported.
partition <- leiden(multiplex_graph, partition_type = "ModularityVertexPartition", resolution_parameter = 0.02, seed = 42)
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
#> Warning in make_py_graph.igraph(r_graph, weights = weights): NAs introduced by coercion to integer range
table(partition)
#> partition
#> 1 2 3 4 5 6
#> 15 13 13 11 8 1
Here we can see partitions in the plotted results are different to as those computed above.
library("graphsim")
library("RColorBrewer")
node.cols <- brewer.pal(max(c(8, partition)),"Pastel1")[partition]
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$lunch, main = "lunch", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[1], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$work, main = "work", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[2], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$facebook, main = "facebook", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[3], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$leisure, main = "leisure", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[4], layout = layout.kamada.kawai)
plot_directed(multiplex_graph$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
