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Running the Leiden algorithm with R on multiplex graphs
In leiden: R Implementation of Leiden Clustering Algorithm
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
knitr::opts_chunk$set(fig.cap = "", fig.path = "Plot")
knitr::opts_chunk$set(fig.align = "center")
options(width = 120, cli.unicode = FALSE, cli.width = 120)
library("reticulate")
module <- py_available() && reticulate::py_module_available("leidenalg") && reticulate::py_module_available("igraph")
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
library("igraph")
suppressWarnings(suppressMessages({
#imported from Achab94/mplex::aarhus_mplex
multiplex_mplex <- list(nodes = structure(list(nodeID = 1:61, nodeLabel = structure(c(3L,
18L, 33L, 4L, 5L, 10L, 11L, 1L, 26L, 27L, 29L, 30L, 32L, 36L,
37L, 40L, 43L, 60L, 12L, 23L, 51L, 56L, 58L, 6L, 13L, 15L, 16L,
24L, 31L, 38L, 42L, 45L, 54L, 55L, 57L, 61L, 2L, 14L, 22L, 19L,
25L, 28L, 34L, 35L, 53L, 7L, 9L, 17L, 41L, 47L, 48L, 52L, 8L,
39L, 49L, 50L, 46L, 44L, 59L, 20L, 21L),
.Label = c("U1", "U10",
"U102", "U106", "U107", "U109", "U110", "U112", "U113", "U118",
"U123", "U124", "U126", "U13", "U130", "U134", "U138", "U139",
"U14", "U140", "U141", "U142", "U17", "U18", "U19", "U21", "U22",
"U23", "U26", "U29", "U3", "U32", "U33", "U37", "U4", "U41",
"U42", "U47", "U48", "U49", "U53", "U54", "U59", "U6", "U62",
"U63", "U65", "U67", "U68", "U69", "U71", "U72", "U73", "U76",
"U79", "U86", "U90", "U91", "U92", "U97", "U99"), class = "factor")),
class = "data.frame",
row.names = c(NA, -61L)), layerNames = c("lunch", "facebook", "coauthor", "leisure", "work"),
L1 = structure(list(ID_Start = c(1L, 1L, 10L, 10L, 10L,
10L, 11L, 11L, 11L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 14L, 15L,
15L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 18L, 18L,
18L, 19L, 19L, 19L, 19L, 20L, 20L, 20L, 21L, 21L, 21L, 22L, 23L,
23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L,
24L, 24L, 24L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 26L,
26L, 26L, 26L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L,
28L, 28L, 28L, 28L, 28L, 28L, 28L, 29L, 29L, 29L, 29L, 29L, 3L,
3L, 3L, 3L, 3L, 30L, 30L, 31L, 31L, 31L, 31L, 32L, 32L, 32L,
33L, 33L, 33L, 34L, 34L, 34L, 35L, 37L, 37L, 38L, 38L, 39L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 40L, 40L, 40L, 41L, 41L, 42L, 43L, 43L,
43L, 44L, 44L, 44L, 44L, 44L, 44L, 44L, 46L, 46L, 46L, 47L, 47L,
47L, 48L, 49L, 49L, 5L, 5L, 5L, 50L, 50L, 51L, 51L, 52L, 53L,
53L, 54L, 54L, 54L, 55L, 55L, 56L, 59L, 6L, 6L, 6L, 6L, 6L, 7L,
7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L,
9L), ID_Arrive = c(2L, 3L, 11L, 14L, 15L, 16L, 14L, 15L, 16L,
13L, 20L, 40L, 20L, 26L, 40L, 45L, 15L, 16L, 30L, 23L, 25L, 46L,
49L, 50L, 51L, 52L, 21L, 25L, 43L, 44L, 56L, 58L, 24L, 25L, 30L,
36L, 40L, 42L, 45L, 44L, 51L, 57L, 26L, 25L, 46L, 49L, 50L, 51L,
52L, 25L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 31L,
35L, 43L, 46L, 47L, 48L, 52L, 56L, 58L, 27L, 34L, 44L, 46L, 31L,
32L, 33L, 34L, 35L, 36L, 38L, 44L, 54L, 59L, 29L, 31L, 32L, 33L,
34L, 35L, 36L, 31L, 32L, 33L, 34L, 35L, 21L, 44L, 51L, 57L, 7L,
34L, 36L, 32L, 33L, 34L, 35L, 33L, 34L, 35L, 34L, 35L, 36L, 35L,
36L, 57L, 58L, 40L, 41L, 39L, 44L, 44L, 10L, 11L, 14L, 15L, 16L,
18L, 6L, 41L, 42L, 45L, 42L, 45L, 45L, 51L, 56L, 58L, 51L, 53L,
54L, 55L, 57L, 59L, 61L, 47L, 49L, 52L, 48L, 51L, 52L, 52L, 50L,
52L, 12L, 13L, 20L, 51L, 52L, 52L, 57L, 56L, 54L, 55L, 55L, 59L,
61L, 59L, 61L, 58L, 61L, 10L, 11L, 14L, 15L, 16L, 21L, 34L, 44L,
51L, 57L, 12L, 13L, 37L, 40L, 41L, 42L, 45L, 18L, 25L, 43L, 51L,
56L, 58L), Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = c(NA, 193L), class = "data.frame"),
L2 = structure(list(ID_Start = c(12L, 12L, 13L, 13L, 13L,
13L, 13L, 13L, 15L, 15L, 15L, 17L, 17L, 17L, 17L, 19L, 19L,
19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 21L, 21L,
21L, 21L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 24L,
24L, 24L, 24L, 24L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L,
26L, 28L, 28L, 28L, 28L, 28L, 29L, 29L, 29L, 29L, 30L, 30L,
30L, 30L, 30L, 31L, 31L, 31L, 31L, 31L, 33L, 33L, 33L, 34L,
34L, 34L, 37L, 37L, 39L, 39L, 39L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 44L, 44L, 46L, 46L, 47L, 47L, 47L, 5L, 5L, 5L, 5L, 50L,
51L, 51L, 56L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L,
8L, 8L, 8L, 8L, 9L, 9L, 9L),
ID_Arrive = c(13L, 23L, 21L,
23L, 26L, 44L, 46L, 51L, 16L, 34L, 39L, 23L, 46L, 47L, 51L,
23L, 24L, 26L, 27L, 28L, 29L, 30L, 31L, 33L, 34L, 56L, 58L,
34L, 44L, 46L, 51L, 34L, 37L, 39L, 44L, 46L, 47L, 50L, 51L,
56L, 28L, 30L, 31L, 33L, 34L, 27L, 28L, 29L, 30L, 33L, 34L,
39L, 44L, 51L, 29L, 30L, 31L, 33L, 34L, 30L, 31L, 33L, 34L,
31L, 33L, 34L, 39L, 44L, 33L, 34L, 37L, 39L, 44L, 34L, 44L,
53L, 39L, 46L, 50L, 39L, 44L, 44L, 46L, 51L, 12L, 13L, 17L,
5L, 7L, 8L, 9L, 46L, 51L, 47L, 51L, 50L, 51L, 56L, 12L, 13L,
19L, 21L, 53L, 56L, 58L, 58L, 13L, 15L, 16L, 21L, 23L, 26L,
30L, 39L, 44L, 51L, 12L, 13L, 21L, 34L, 37L, 51L, 56L, 58L
),
Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = 194:317, class = "data.frame"),
L3 = structure(list(ID_Start = c(10L, 12L, 18L, 23L, 23L,
23L, 26L, 26L, 26L, 26L, 26L, 28L, 30L, 38L, 39L, 4L, 46L,
46L, 49L, 6L, 8L),
ID_Arrive = c(11L, 13L, 46L, 46L, 49L,
52L, 27L, 28L, 30L, 33L, 36L, 33L, 36L, 54L, 55L, 6L, 48L,
49L, 52L, 14L, 37L),
Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = 318:338, class = "data.frame"),
L4 = structure(list(ID_Start = c(10L, 12L, 12L, 15L, 15L,
15L, 17L, 17L, 17L, 17L, 19L, 19L, 19L, 19L, 20L, 20L, 20L,
20L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 24L,
24L, 24L, 24L, 25L, 25L, 25L, 25L, 28L, 28L, 28L, 29L, 29L,
30L, 31L, 31L, 31L, 31L, 32L, 33L, 33L, 34L, 34L, 34L, 34L,
35L, 37L, 37L, 37L, 37L, 39L, 39L, 4L, 4L, 40L, 40L, 40L,
41L, 41L, 42L, 44L, 46L, 46L, 46L, 46L, 47L, 47L, 48L, 5L,
5L, 5L, 50L, 55L, 6L, 8L, 8L, 8L, 8L, 8L, 9L),
ID_Arrive = c(15L,
13L, 25L, 16L, 34L, 39L, 23L, 46L, 50L, 52L, 23L, 25L, 28L,
36L, 23L, 40L, 42L, 45L, 25L, 31L, 35L, 46L, 47L, 48L, 49L,
50L, 52L, 56L, 25L, 31L, 33L, 35L, 31L, 35L, 46L, 56L, 32L,
33L, 36L, 31L, 35L, 33L, 33L, 34L, 35L, 37L, 33L, 34L, 35L,
35L, 36L, 45L, 50L, 58L, 38L, 39L, 43L, 45L, 43L, 55L, 14L,
6L, 41L, 42L, 45L, 42L, 45L, 45L, 51L, 47L, 48L, 50L, 51L,
48L, 50L, 52L, 13L, 20L, 23L, 52L, 61L, 14L, 11L, 37L, 40L,
42L, 45L, 25L),
Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L)), row.names = 339:426, class = "data.frame"),
L5 = structure(list(ID_Start = c(10L, 10L, 10L, 10L, 11L,
11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 12L, 13L, 13L,
13L, 13L, 13L, 13L, 13L, 15L, 17L, 17L, 17L, 18L, 18L, 18L,
19L, 19L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 20L,
20L, 20L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 23L, 23L,
23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 25L, 25L, 25L, 26L,
26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 27L, 27L, 28L,
29L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 30L, 30L, 31L, 31L,
31L, 31L, 31L, 32L, 33L, 34L, 34L, 34L, 35L, 36L, 37L, 37L,
37L, 37L, 38L, 38L, 38L, 39L, 39L, 4L, 4L, 4L, 4L, 40L, 40L,
40L, 41L, 41L, 42L, 43L, 44L, 44L, 44L, 44L, 44L, 44L, 44L,
46L, 46L, 46L, 46L, 46L, 47L, 47L, 48L, 5L, 5L, 5L, 5L, 5L,
50L, 50L, 51L, 51L, 51L, 51L, 53L, 54L, 55L, 6L, 6L, 6L,
6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L,
8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L),
ID_Arrive = c(11L, 14L,
15L, 16L, 13L, 15L, 16L, 18L, 21L, 26L, 34L, 46L, 60L, 13L,
20L, 18L, 20L, 22L, 26L, 40L, 45L, 46L, 34L, 23L, 46L, 51L,
21L, 44L, 51L, 26L, 44L, 11L, 12L, 18L, 21L, 37L, 40L, 41L,
5L, 51L, 7L, 8L, 40L, 42L, 45L, 40L, 41L, 44L, 46L, 51L,
57L, 58L, 60L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 26L, 31L,
32L, 46L, 51L, 56L, 27L, 28L, 30L, 31L, 32L, 33L, 34L, 36L,
37L, 44L, 36L, 44L, 32L, 35L, 11L, 21L, 44L, 46L, 51L, 57L,
6L, 7L, 9L, 32L, 36L, 34L, 35L, 38L, 41L, 44L, 33L, 44L,
36L, 44L, 46L, 44L, 44L, 40L, 41L, 42L, 45L, 44L, 54L, 59L,
44L, 55L, 11L, 14L, 6L, 7L, 41L, 42L, 45L, 42L, 45L, 45L,
51L, 51L, 53L, 54L, 55L, 57L, 59L, 61L, 47L, 48L, 49L, 51L,
52L, 48L, 51L, 51L, 12L, 13L, 20L, 21L, 22L, 51L, 52L, 52L,
56L, 57L, 58L, 55L, 56L, 61L, 11L, 14L, 18L, 21L, 35L, 51L,
7L, 10L, 11L, 15L, 16L, 18L, 19L, 20L, 21L, 26L, 28L, 29L,
30L, 31L, 32L, 33L, 34L, 35L, 36L, 39L, 44L, 46L, 51L, 57L,
11L, 13L, 19L, 21L, 26L, 34L, 37L, 40L, 41L, 42L, 45L, 51L
),
Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L)), row.names = 427:620, class = "data.frame"))
lunch <- graph_from_edgelist(as.matrix(multiplex_mplex[[3]][,1:2]))
V(lunch)$name <- as.character(multiplex_mplex[[1]][,2])
facebook <- graph_from_edgelist(as.matrix(multiplex_mplex[[4]][,1:2]))
facebook <- graph_from_edgelist(
rbind(as.matrix(multiplex_mplex[[4]][,1:2]),
cbind(setdiff(as.integer(V(lunch)), as.integer(V(facebook))),
setdiff(as.integer(V(lunch)), as.integer(V(facebook))))
)
)
V(facebook)$name <- as.character(multiplex_mplex[[1]][,2])
coauthor <- graph_from_edgelist(as.matrix(multiplex_mplex[[5]][,1:2]))
coauthor <- graph_from_edgelist(
rbind(as_edgelist(coauthor),
cbind(setdiff(as.integer(V(lunch)), as.integer(V(coauthor))),
setdiff(as.integer(V(lunch)), as.integer(V(coauthor))))
)
)
leisure <- graph_from_edgelist(as.matrix(multiplex_mplex[[6]][,1:2]))
V(leisure)$name <- as.character(multiplex_mplex[[1]][,2])
work <- graph_from_edgelist(as.matrix(multiplex_mplex[[7]][,1:2]))
V(work)$name <- as.character(multiplex_mplex[[1]][,2])
multiplex_graph <- list(lunch, facebook, coauthor, leisure, work)
multiplex_graph <- lapply(multiplex_graph, upgrade_graph)
names(multiplex_graph) <- c("lunch", "facebook", "coauthor", "leisure", "work")
}))
multiplex_graph
Usage
Multiplex graph objects
Now we have a multiplex graph structure. This multiplex graph is a list of different igraph object, in the case representing different relationships between the sample people.
names(multiplex_graph)
Here we import a plotting function to display these 5 groups.
library("graphsim")
library("RColorBrewer")
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$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
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)
partition <- c(4, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 2, 2, 3, 3, 3, 1, 1, 1, 2,
1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2,
2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1)
table(partition)
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$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
This can also be run on a list of adjacency matrices giving the same results.
partition <- leiden(multiplex_matrix,
partition_type = "CPMVertexPartition",
resolution_parameter = 0.025,
seed = 9001)
partition <- c(4, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 2, 2, 3, 3, 3, 1, 1, 1, 2,
1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2,
2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1)
table(partition)
Fine-tuning with resolution
The resolution parameter applies on multiplex graphs to fine-tuning how many clusters are detected.
partition <- leiden(multiplex_graph, partition_type = "CPMVertexPartition", resolution_parameter = 0.1, seed = 42)
partition <- c(8, 2, 6, 4, 2, 4, 6, 2, 7, 4, 4, 2, 2, 4, 4, 4, 3, 6, 1, 2,
6, 10, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 2,
2, 2, 7, 6, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 3, 6, 7, 5, 9, 5)
table(partition)
library("graphsim")
library("RColorBrewer")
node.cols <- brewer.pal(min(c(9, partition)),"Pastel1")[partition]
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$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)
partition <- c(11, 11, 5, 4, 8, 4, 5, 3, 6, 4, 4, 8, 8, 4, 4, 4, 1, 5, 7,
3, 5, 8, 1, 2, 6, 7, 7, 2, 2, 7, 2, 2, 2, 2, 2, 7, 3, 10, 9,
3, 3, 3, 6, 5, 3, 1, 1, 13, 1, 1, 1, 1, 9, 10, 9, 6, 5, 6, 10,
12, 9)
table(partition)
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$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
Multiplex cost functions
Any defined cost function is supported for multiplex graphs.
For example, the Modularity Vertex Partition is also supported.
partition <- leiden(multiplex_graph, partition_type = "ModularityVertexPartition", resolution_parameter = 0.02, seed = 42)
partition <- c(4, 3, 4, 4, 3, 4, 4, 3, 1, 4, 4, 3, 3, 4, 4, 4, 1, 1, 2, 3,
3, 3, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 3, 3,
3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 4, 1, 5, 6, 5)
table(partition)
Here we can see partitions in the plotted results are different to as those computed above.
library("graphsim")
library("RColorBrewer")
node.cols <- brewer.pal(max(c(8, partition)),"Pastel1")[partition]
par(mfrow = c(2, 3))
plot_directed(multiplex_graph$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)
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leiden documentation built on Nov. 17, 2023, 5:08 p.m.
R Package Documentation
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knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) knitr::opts_chunk$set(fig.cap = "", fig.path = "Plot") knitr::opts_chunk$set(fig.align = "center") options(width = 120, cli.unicode = FALSE, cli.width = 120) library("reticulate") module <- py_available() && reticulate::py_module_available("leidenalg") && reticulate::py_module_available("igraph")
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
library("igraph") suppressWarnings(suppressMessages({ #imported from Achab94/mplex::aarhus_mplex multiplex_mplex <- list(nodes = structure(list(nodeID = 1:61, nodeLabel = structure(c(3L, 18L, 33L, 4L, 5L, 10L, 11L, 1L, 26L, 27L, 29L, 30L, 32L, 36L, 37L, 40L, 43L, 60L, 12L, 23L, 51L, 56L, 58L, 6L, 13L, 15L, 16L, 24L, 31L, 38L, 42L, 45L, 54L, 55L, 57L, 61L, 2L, 14L, 22L, 19L, 25L, 28L, 34L, 35L, 53L, 7L, 9L, 17L, 41L, 47L, 48L, 52L, 8L, 39L, 49L, 50L, 46L, 44L, 59L, 20L, 21L), .Label = c("U1", "U10", "U102", "U106", "U107", "U109", "U110", "U112", "U113", "U118", "U123", "U124", "U126", "U13", "U130", "U134", "U138", "U139", "U14", "U140", "U141", "U142", "U17", "U18", "U19", "U21", "U22", "U23", "U26", "U29", "U3", "U32", "U33", "U37", "U4", "U41", "U42", "U47", "U48", "U49", "U53", "U54", "U59", "U6", "U62", "U63", "U65", "U67", "U68", "U69", "U71", "U72", "U73", "U76", "U79", "U86", "U90", "U91", "U92", "U97", "U99"), class = "factor")), class = "data.frame", row.names = c(NA, -61L)), layerNames = c("lunch", "facebook", "coauthor", "leisure", "work"), L1 = structure(list(ID_Start = c(1L, 1L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 14L, 15L, 15L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 18L, 18L, 18L, 19L, 19L, 19L, 19L, 20L, 20L, 20L, 21L, 21L, 21L, 22L, 23L, 23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 26L, 26L, 26L, 26L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 28L, 28L, 28L, 28L, 28L, 28L, 28L, 29L, 29L, 29L, 29L, 29L, 3L, 3L, 3L, 3L, 3L, 30L, 30L, 31L, 31L, 31L, 31L, 32L, 32L, 32L, 33L, 33L, 33L, 34L, 34L, 34L, 35L, 37L, 37L, 38L, 38L, 39L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 40L, 40L, 40L, 41L, 41L, 42L, 43L, 43L, 43L, 44L, 44L, 44L, 44L, 44L, 44L, 44L, 46L, 46L, 46L, 47L, 47L, 47L, 48L, 49L, 49L, 5L, 5L, 5L, 50L, 50L, 51L, 51L, 52L, 53L, 53L, 54L, 54L, 54L, 55L, 55L, 56L, 59L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L), ID_Arrive = c(2L, 3L, 11L, 14L, 15L, 16L, 14L, 15L, 16L, 13L, 20L, 40L, 20L, 26L, 40L, 45L, 15L, 16L, 30L, 23L, 25L, 46L, 49L, 50L, 51L, 52L, 21L, 25L, 43L, 44L, 56L, 58L, 24L, 25L, 30L, 36L, 40L, 42L, 45L, 44L, 51L, 57L, 26L, 25L, 46L, 49L, 50L, 51L, 52L, 25L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 31L, 35L, 43L, 46L, 47L, 48L, 52L, 56L, 58L, 27L, 34L, 44L, 46L, 31L, 32L, 33L, 34L, 35L, 36L, 38L, 44L, 54L, 59L, 29L, 31L, 32L, 33L, 34L, 35L, 36L, 31L, 32L, 33L, 34L, 35L, 21L, 44L, 51L, 57L, 7L, 34L, 36L, 32L, 33L, 34L, 35L, 33L, 34L, 35L, 34L, 35L, 36L, 35L, 36L, 57L, 58L, 40L, 41L, 39L, 44L, 44L, 10L, 11L, 14L, 15L, 16L, 18L, 6L, 41L, 42L, 45L, 42L, 45L, 45L, 51L, 56L, 58L, 51L, 53L, 54L, 55L, 57L, 59L, 61L, 47L, 49L, 52L, 48L, 51L, 52L, 52L, 50L, 52L, 12L, 13L, 20L, 51L, 52L, 52L, 57L, 56L, 54L, 55L, 55L, 59L, 61L, 59L, 61L, 58L, 61L, 10L, 11L, 14L, 15L, 16L, 21L, 34L, 44L, 51L, 57L, 12L, 13L, 37L, 40L, 41L, 42L, 45L, 18L, 25L, 43L, 51L, 56L, 58L), Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = c(NA, 193L), class = "data.frame"), L2 = structure(list(ID_Start = c(12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 15L, 15L, 15L, 17L, 17L, 17L, 17L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 21L, 21L, 21L, 21L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 24L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 28L, 28L, 28L, 28L, 28L, 29L, 29L, 29L, 29L, 30L, 30L, 30L, 30L, 30L, 31L, 31L, 31L, 31L, 31L, 33L, 33L, 33L, 34L, 34L, 34L, 37L, 37L, 39L, 39L, 39L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 44L, 44L, 46L, 46L, 47L, 47L, 47L, 5L, 5L, 5L, 5L, 50L, 51L, 51L, 56L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L), ID_Arrive = c(13L, 23L, 21L, 23L, 26L, 44L, 46L, 51L, 16L, 34L, 39L, 23L, 46L, 47L, 51L, 23L, 24L, 26L, 27L, 28L, 29L, 30L, 31L, 33L, 34L, 56L, 58L, 34L, 44L, 46L, 51L, 34L, 37L, 39L, 44L, 46L, 47L, 50L, 51L, 56L, 28L, 30L, 31L, 33L, 34L, 27L, 28L, 29L, 30L, 33L, 34L, 39L, 44L, 51L, 29L, 30L, 31L, 33L, 34L, 30L, 31L, 33L, 34L, 31L, 33L, 34L, 39L, 44L, 33L, 34L, 37L, 39L, 44L, 34L, 44L, 53L, 39L, 46L, 50L, 39L, 44L, 44L, 46L, 51L, 12L, 13L, 17L, 5L, 7L, 8L, 9L, 46L, 51L, 47L, 51L, 50L, 51L, 56L, 12L, 13L, 19L, 21L, 53L, 56L, 58L, 58L, 13L, 15L, 16L, 21L, 23L, 26L, 30L, 39L, 44L, 51L, 12L, 13L, 21L, 34L, 37L, 51L, 56L, 58L ), Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = 194:317, class = "data.frame"), L3 = structure(list(ID_Start = c(10L, 12L, 18L, 23L, 23L, 23L, 26L, 26L, 26L, 26L, 26L, 28L, 30L, 38L, 39L, 4L, 46L, 46L, 49L, 6L, 8L), ID_Arrive = c(11L, 13L, 46L, 46L, 49L, 52L, 27L, 28L, 30L, 33L, 36L, 33L, 36L, 54L, 55L, 6L, 48L, 49L, 52L, 14L, 37L), Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = 318:338, class = "data.frame"), L4 = structure(list(ID_Start = c(10L, 12L, 12L, 15L, 15L, 15L, 17L, 17L, 17L, 17L, 19L, 19L, 19L, 19L, 20L, 20L, 20L, 20L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 25L, 25L, 25L, 25L, 28L, 28L, 28L, 29L, 29L, 30L, 31L, 31L, 31L, 31L, 32L, 33L, 33L, 34L, 34L, 34L, 34L, 35L, 37L, 37L, 37L, 37L, 39L, 39L, 4L, 4L, 40L, 40L, 40L, 41L, 41L, 42L, 44L, 46L, 46L, 46L, 46L, 47L, 47L, 48L, 5L, 5L, 5L, 50L, 55L, 6L, 8L, 8L, 8L, 8L, 8L, 9L), ID_Arrive = c(15L, 13L, 25L, 16L, 34L, 39L, 23L, 46L, 50L, 52L, 23L, 25L, 28L, 36L, 23L, 40L, 42L, 45L, 25L, 31L, 35L, 46L, 47L, 48L, 49L, 50L, 52L, 56L, 25L, 31L, 33L, 35L, 31L, 35L, 46L, 56L, 32L, 33L, 36L, 31L, 35L, 33L, 33L, 34L, 35L, 37L, 33L, 34L, 35L, 35L, 36L, 45L, 50L, 58L, 38L, 39L, 43L, 45L, 43L, 55L, 14L, 6L, 41L, 42L, 45L, 42L, 45L, 45L, 51L, 47L, 48L, 50L, 51L, 48L, 50L, 52L, 13L, 20L, 23L, 52L, 61L, 14L, 11L, 37L, 40L, 42L, 45L, 25L), Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = 339:426, class = "data.frame"), L5 = structure(list(ID_Start = c(10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 15L, 17L, 17L, 17L, 18L, 18L, 18L, 19L, 19L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 20L, 20L, 20L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 25L, 25L, 25L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 27L, 27L, 28L, 29L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 30L, 30L, 31L, 31L, 31L, 31L, 31L, 32L, 33L, 34L, 34L, 34L, 35L, 36L, 37L, 37L, 37L, 37L, 38L, 38L, 38L, 39L, 39L, 4L, 4L, 4L, 4L, 40L, 40L, 40L, 41L, 41L, 42L, 43L, 44L, 44L, 44L, 44L, 44L, 44L, 44L, 46L, 46L, 46L, 46L, 46L, 47L, 47L, 48L, 5L, 5L, 5L, 5L, 5L, 50L, 50L, 51L, 51L, 51L, 51L, 53L, 54L, 55L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L), ID_Arrive = c(11L, 14L, 15L, 16L, 13L, 15L, 16L, 18L, 21L, 26L, 34L, 46L, 60L, 13L, 20L, 18L, 20L, 22L, 26L, 40L, 45L, 46L, 34L, 23L, 46L, 51L, 21L, 44L, 51L, 26L, 44L, 11L, 12L, 18L, 21L, 37L, 40L, 41L, 5L, 51L, 7L, 8L, 40L, 42L, 45L, 40L, 41L, 44L, 46L, 51L, 57L, 58L, 60L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 26L, 31L, 32L, 46L, 51L, 56L, 27L, 28L, 30L, 31L, 32L, 33L, 34L, 36L, 37L, 44L, 36L, 44L, 32L, 35L, 11L, 21L, 44L, 46L, 51L, 57L, 6L, 7L, 9L, 32L, 36L, 34L, 35L, 38L, 41L, 44L, 33L, 44L, 36L, 44L, 46L, 44L, 44L, 40L, 41L, 42L, 45L, 44L, 54L, 59L, 44L, 55L, 11L, 14L, 6L, 7L, 41L, 42L, 45L, 42L, 45L, 45L, 51L, 51L, 53L, 54L, 55L, 57L, 59L, 61L, 47L, 48L, 49L, 51L, 52L, 48L, 51L, 51L, 12L, 13L, 20L, 21L, 22L, 51L, 52L, 52L, 56L, 57L, 58L, 55L, 56L, 61L, 11L, 14L, 18L, 21L, 35L, 51L, 7L, 10L, 11L, 15L, 16L, 18L, 19L, 20L, 21L, 26L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 39L, 44L, 46L, 51L, 57L, 11L, 13L, 19L, 21L, 26L, 34L, 37L, 40L, 41L, 42L, 45L, 51L ), Weight = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), row.names = 427:620, class = "data.frame")) lunch <- graph_from_edgelist(as.matrix(multiplex_mplex[[3]][,1:2])) V(lunch)$name <- as.character(multiplex_mplex[[1]][,2]) facebook <- graph_from_edgelist(as.matrix(multiplex_mplex[[4]][,1:2])) facebook <- graph_from_edgelist( rbind(as.matrix(multiplex_mplex[[4]][,1:2]), cbind(setdiff(as.integer(V(lunch)), as.integer(V(facebook))), setdiff(as.integer(V(lunch)), as.integer(V(facebook)))) ) ) V(facebook)$name <- as.character(multiplex_mplex[[1]][,2]) coauthor <- graph_from_edgelist(as.matrix(multiplex_mplex[[5]][,1:2])) coauthor <- graph_from_edgelist( rbind(as_edgelist(coauthor), cbind(setdiff(as.integer(V(lunch)), as.integer(V(coauthor))), setdiff(as.integer(V(lunch)), as.integer(V(coauthor)))) ) ) leisure <- graph_from_edgelist(as.matrix(multiplex_mplex[[6]][,1:2])) V(leisure)$name <- as.character(multiplex_mplex[[1]][,2]) work <- graph_from_edgelist(as.matrix(multiplex_mplex[[7]][,1:2])) V(work)$name <- as.character(multiplex_mplex[[1]][,2]) multiplex_graph <- list(lunch, facebook, coauthor, leisure, work) multiplex_graph <- lapply(multiplex_graph, upgrade_graph) names(multiplex_graph) <- c("lunch", "facebook", "coauthor", "leisure", "work") })) multiplex_graph
Usage
Multiplex graph objects
Now we have a multiplex graph structure. This multiplex graph is a list of different igraph object, in the case representing different relationships between the sample people.
names(multiplex_graph)
Here we import a plotting function to display these 5 groups.
library("graphsim") library("RColorBrewer") par(mfrow = c(2, 3)) plot_directed(multiplex_graph$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
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)
partition <- c(4, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 2, 2, 3, 3, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1)
table(partition)
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$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
This can also be run on a list of adjacency matrices giving the same results.
partition <- leiden(multiplex_matrix, partition_type = "CPMVertexPartition", resolution_parameter = 0.025, seed = 9001)
partition <- c(4, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 2, 2, 3, 3, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1)
table(partition)
Fine-tuning with resolution
The resolution parameter applies on multiplex graphs to fine-tuning how many clusters are detected.
partition <- leiden(multiplex_graph, partition_type = "CPMVertexPartition", resolution_parameter = 0.1, seed = 42)
partition <- c(8, 2, 6, 4, 2, 4, 6, 2, 7, 4, 4, 2, 2, 4, 4, 4, 3, 6, 1, 2, 6, 10, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 2, 2, 2, 7, 6, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 3, 6, 7, 5, 9, 5)
table(partition)
library("graphsim") library("RColorBrewer") node.cols <- brewer.pal(min(c(9, partition)),"Pastel1")[partition] par(mfrow = c(2, 3)) plot_directed(multiplex_graph$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)
partition <- c(11, 11, 5, 4, 8, 4, 5, 3, 6, 4, 4, 8, 8, 4, 4, 4, 1, 5, 7, 3, 5, 8, 1, 2, 6, 7, 7, 2, 2, 7, 2, 2, 2, 2, 2, 7, 3, 10, 9, 3, 3, 3, 6, 5, 3, 1, 1, 13, 1, 1, 1, 1, 9, 10, 9, 6, 5, 6, 10, 12, 9)
table(partition)
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$coauthor, main = "coauthor", col.label = node.cols, col.arrow = brewer.pal(5, "Pastel1")[5], layout = layout.kamada.kawai)
Multiplex cost functions
Any defined cost function is supported for multiplex graphs. For example, the Modularity Vertex Partition is also supported.
partition <- leiden(multiplex_graph, partition_type = "ModularityVertexPartition", resolution_parameter = 0.02, seed = 42)
partition <- c(4, 3, 4, 4, 3, 4, 4, 3, 1, 4, 4, 3, 3, 4, 4, 4, 1, 1, 2, 3, 3, 3, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 3, 3, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 4, 1, 5, 6, 5)
table(partition)
Here we can see partitions in the plotted results are different to as those computed above.
library("graphsim") library("RColorBrewer") node.cols <- brewer.pal(max(c(8, partition)),"Pastel1")[partition] par(mfrow = c(2, 3)) plot_directed(multiplex_graph$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)
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