Manipulation and plotting accessories for igraph objects
You may easily fetch the package via devtools:
devtools::install_github('PiotrTymoszuk/graphExtra')
The package is available under a GPL-3 license.
The package maintainer is Piotr Tymoszuk.
Many thanks to authors, maintainers and contributors of the tidyverse evironment, and packages igraph, ggnetwork, and ggtext.
The package offers few functional tools that may help to integrate great tools of igraph in tidyverse-styled analysis pipelines:
as_iGraph(): generatesigraphobjects from a wide range of similarity and distance matrices as well as numeric matrices and data frames with similarity or correlation metrics defined by the userprune_degree(),select_vertices(), andprune_vertices()allow for selection or removal of graph vertices based on a degree cutoff or logical expressionssplit_vertices()splits a graph into sub-graphs by levels of one or more vertex attributes; this may be especially interesting for detailed analyses of communitiesget_vertex_attributes()andset_vertex_attributes()let the user fetch and set multiple vertex attributes with a data frame or a tibbleadd_community()merges the community information obtained with one of the clustering tools offered byigraphpackage with vertex attributessummary()computes a bunch of common vertex importance statistics such as degree, betweenness, and hub scoreplot()overwrites the respective default method to generateggplot-compatible graphics forigraphobjectsneighbor_graph()andneighbor_attr()extract the neighborhood of a vertex of interest and the neighborhood attributes, respectively
In the following example, we will investigate a similarity network of cars in
the Cars93 data set provided with the MASS package.
The input data for the similarity graph are numeric features such as number of cylinders, car dimensions,
or price.
The car's make and classification (small, compact, midsize, large, van, sporty) will serve as vertex attributes.
## required packages
library(tidyverse)
library(igraph)
library(graphExtra)
library(patchwork) ## for multi-plot panels
## numeric data used for network construction
numeric_cars <-
MASS::Cars93[, c("Make",
"Min.Price", "Max.Price",
"MPG.city", "MPG.highway",
"Cylinders", "EngineSize", "Horsepower",
"Rev.per.mile", "Fuel.tank.capacity",
"Passengers",
"Length", "Wheelbase",
"Width", "Turn.circle",
"Rear.seat.room", "Luggage.room",
"Weight")]
numeric_cars <- numeric_cars %>%
mutate(Cylinders = as.numeric(Cylinders)) %>%
column_to_rownames('Make')
## cars' attributes
car_attributes <-
MASS::Cars93[, c("Make", "Type")] %>%
mutate(Type = fct_relevel(Type,
"Small", "Compact", "Midsize",
"Large", "Van", "Sporty"))
The network is constructed with function as_iGraph() which takes a range of different objects
and converts them to non-directional igraph graphs.
The possible inputs are data frames, data matrices, correlation matrices, or distances.
Please note that any NA values in the similarity matrix make computation impossible.
The user can choose to fill them with a numeric value or rows/columns with NA values.
In the code below, the TauB correlation matrix of cars has NAs.
They are differently handled by as_iGraph(), which results in differences in network's dimensions:
tau_mtx <- numeric_cars %>%
t %>%
cor(method = 'kendall')
## ignoring: throws an error
> tau_mtx %>%
+ as_iGraph(input_type = 'similarity',
+ na_action = "ignore")
Error: There are NA values in the similarity matrix.
## filling with 0
> tau_mtx %>%
+ as_iGraph(input_type = 'similarity',
+ na_action = "pad",
+ na_pad_value = 0) %>%
+ dimensions
vertices edges
93 3321
Warning message:
There are 1914 NA values in the similarity matrix. They are padded with 0
## row/column-wise removal
> tau_mtx %>%
+ as_iGraph(input_type = 'similarity',
+ na_action = "remove") %>%
+ dimensions
vertices edges
82 3321
Warning message:
There are 1914 NA values in the similarity matrix. They amount to 11 incomplete rows, which will be removed.
For further analyses, we will construct a weighted network with a similarity measure derived from Manhattan distances between the cars. We choose a cutoff 0.9 of the similarity statistics, which means that the network's edges will be defined by pairwise associations between cars with similarity of 0.9 and larger:
## graph object from a distance object of Manhattan distances:
## min/max normalization of the distances, selection of
## the strongest associations
## The object will be used in later analyses
dist_mtx <- numeric_cars %>%
dist(method = 'manhattan')
norm_function <- function(x) {
1 - (x - min(x, na.rm = TRUE))/(max(x, na.rm = TRUE) - min(x, na.rm = TRUE))
}
car_network <-
as_iGraph(dist_mtx,
fun = norm_function,
cutoff = 0.9,
diag = FALSE)
In our car's network there are two cars (Geo Metro and Volkswagen Eurovan)
without neighbors, i.e. with no similarity of 0.9 or larger with any other cars.
If desired, such isolated vertices can be easily removed with function prune_degree(),
which removes all vertices with degree/neighbor number lower than a cutoff value:
## there are vertices with no neighbors
car_degrees <- degree(car_network)
car_network <- prune_degree(car_network, cutoff = 0)
> car_degrees[car_degrees == 0]
Geo Metro Volkswagen Eurovan
0 0
By default, there are two vertex attributes in the graph: the vertex' index and
name.
The user can set additional attributes from a data frame with set_vertex_attributes()
function.
The attributes are matched with the vertices by the first column of the
attribute data frame, which is expected to contain the vertex' names.
To obtain vertex attributes, please call get_vertex_attributes():
## default vertex attributes
> get_vertex_attributes(car_network)
# A tibble: 91 × 2
index name
<int> <chr>
1 1 Acura Integra
2 2 Acura Legend
3 3 Audi 90
4 4 Audi 100
5 5 BMW 535i
6 6 Buick Century
7 7 Buick LeSabre
8 8 Buick Roadmaster
9 9 Buick Riviera
10 10 Cadillac DeVille
# ℹ 81 more rows
# ℹ Use `print(n = ...)` to see more rows
## setting additional vertex attributes:
## car type
car_network <-
set_vertex_attributes(car_network, car_attributes)
## type was set as the new attribute
> get_vertex_attributes(car_network)
# A tibble: 91 × 3
index name Type
<int> <chr> <fct>
1 1 Acura Integra Small
2 2 Acura Legend Midsize
3 3 Audi 90 Compact
4 4 Audi 100 Midsize
5 5 BMW 535i Midsize
6 6 Buick Century Midsize
7 7 Buick LeSabre Large
8 8 Buick Roadmaster Large
9 9 Buick Riviera Midsize
10 10 Cadillac DeVille Large
# ℹ 81 more rows
# ℹ Use `print(n = ...)` to see more rows
The igraph package offers a broad palette of tools for community detection,
including the popular Leiden algorithm
implemented by cluster_leiden() function.
## definition of communities by Leiden method
set.seed(5467)
car_communities <-
cluster_leiden(car_network,
objective_function = 'modularity',
resolution = 0.5,
n_iterations = 100)
Our graphExtra package provides tools for re-naming of communities (comm_recode()),
community assignment and size computation (assignment() and sizes()),
merging small communities together (comm_lump()):
## re-coding names of the communities
car_communities <-
comm_recode(car_communities,
new_names = c('#1' = '1',
'#2' = '2',
'#3' = '3',
'#4' = '4'))
## lumping small communities with less than 7 cars together
car_communities <- car_communities %>%
comm_lump(cutoff = 7, other_name = 'other')
> assignment(car_communities)
# A tibble: 91 × 3
index name community_id
<int> <chr> <fct>
1 1 Acura Integra #1
2 2 Acura Legend #2
3 3 Audi 90 #2
4 4 Audi 100 #2
5 5 BMW 535i #2
6 6 Buick Century #1
7 7 Buick LeSabre #2
8 8 Buick Roadmaster other
9 9 Buick Riviera #2
10 10 Cadillac DeVille #2
# ℹ 81 more rows
# ℹ Use `print(n = ...)` to see more rows
> sizes(car_communities)
Community sizes
1 2 3 4
44 36 8 3
An easy way to add the community assignment to the network is to call add_communities(),
which sets the community label as the vertex attribute community_id:
car_network <- car_network %>%
add_communities(car_communities)
> get_vertex_attributes(car_network)
# A tibble: 91 × 4
index name Type community_id
<int> <chr> <fct> <fct>
1 1 Acura Integra Small #1
2 2 Acura Legend Midsize #2
3 3 Audi 90 Compact #2
4 4 Audi 100 Midsize #2
5 5 BMW 535i Midsize #2
6 6 Buick Century Midsize #1
7 7 Buick LeSabre Large #2
8 8 Buick Roadmaster Large other
9 9 Buick Riviera Midsize #2
10 10 Cadillac DeVille Large #2
# ℹ 81 more rows
# ℹ Use `print(n = ...)` to see more rows
Transformation of the network: pruning, selecting, and splitting vertices by attributes. Vertex's neighbors
Vertices can be removed or selected by their attributes or any other logical expressions
with functions prune_vertices() and select_vertices():
## removal of of nodes in the 'other' community
car_network <- car_network %>%
prune_vertices(community_id == 'other')
## vertex attributes for car types
> car_network %>%
+ select_vertices(Type %in% c('Large', 'Van')) %>%
+ get_vertex_attributes
# A tibble: 16 × 4
index name Type community_id
<int> <chr> <fct> <fct>
1 1 Buick LeSabre Large #2
2 2 Cadillac DeVille Large #2
3 3 Chevrolet Lumina_APV Van #2
4 4 Chevrolet Astro Van #2
5 5 Chrylser Concorde Large #2
6 6 Chrysler Imperial Large #2
7 7 Dodge Caravan Van #2
8 8 Eagle Vision Large #2
9 9 Ford Aerostar Van #2
10 10 Lincoln Town_Car Large #2
11 11 Mazda MPV Van #2
12 12 Nissan Quest Van #2
13 13 Oldsmobile Silhouette Van #2
14 14 Oldsmobile Eighty-Eight Large #2
15 15 Pontiac Bonneville Large #2
16 16 Toyota Previa Van #2
> car_network %>%
+ select_vertices(Type %in% c('Small', 'Compact')) %>%
+ get_vertex_attributes
# A tibble: 36 × 4
index name Type community_id
<int> <chr> <fct> <fct>
1 1 Acura Integra Small #1
2 2 Audi 90 Compact #2
3 3 Chevrolet Cavalier Compact #1
4 4 Chevrolet Corsica Compact #1
5 5 Chrysler LeBaron Compact #1
6 6 Dodge Colt Small #4
7 7 Dodge Shadow Small #1
8 8 Dodge Spirit Compact #1
9 9 Eagle Summit Small #1
10 10 Ford Festiva Small #4
# ℹ 26 more rows
# ℹ Use `print(n = ...)` to see more rows
Function split_vertices() generates a list of sub-graphs defined by levels
of a vertex attribute.
Here, we create a list of sub-plots for each of the communities:
> car_network %>%
+ split_vertices(community_id)
$`#1`
IGRAPH 957a0bc UNW- 44 378 --
+ attr: name (v/c), Type (v/x), community_id (v/x), degree (v/n), betweenness (v/n), hub_score (v/n), transitivity
| (v/n), top_car (v/c), weight (e/n)
+ edges from 957a0bc (vertex names):
[1] Acura Integra--Chevrolet Corsica Acura Integra--Dodge Shadow Acura Integra--Ford Tempo
[4] Acura Integra--Honda Prelude Acura Integra--Hyundai Elantra Acura Integra--Pontiac Sunbird
[7] Acura Integra--Saab 900 Buick Century--Chevrolet Corsica Buick Century--Chevrolet Lumina
[10] Buick Century--Dodge Shadow Buick Century--Dodge Spirit Buick Century--Dodge Dynasty
[13] Buick Century--Ford Tempo Buick Century--Ford Mustang Buick Century--Ford Probe
[16] Buick Century--Honda Prelude Buick Century--Honda Accord Buick Century--Hyundai Elantra
[19] Buick Century--Hyundai Sonata Buick Century--Mazda 626 Buick Century--Mercedes-Benz 190E
+ ... omitted several edges
$`#2`
IGRAPH 957a1a0 UNW- 36 178 --
+ attr: name (v/c), Type (v/x), community_id (v/x), degree (v/n), betweenness (v/n), hub_score (v/n), transitivity
| (v/n), top_car (v/c), weight (e/n)
+ edges from 957a1a0 (vertex names):
[1] Acura Legend --Audi 90 Acura Legend --Audi 100 Acura Legend --BMW 535i
[4] Acura Legend --Chrylser Concorde Acura Legend --Eagle Vision Acura Legend --Lexus ES300
[7] Acura Legend --Lexus SC300 Acura Legend --Mazda MPV Acura Legend --Mercedes-Benz 300E
[10] Acura Legend --Mitsubishi Diamante Audi 90 --Audi 100 Audi 90 --Lexus ES300
[13] Audi 90 --Lexus SC300 Audi 90 --Mazda MPV Audi 90 --Mercedes-Benz 300E
[16] Audi 90 --Mitsubishi Diamante Audi 90 --Nissan Maxima Audi 100 --BMW 535i
[19] Audi 100 --Lexus ES300 Audi 100 --Lexus SC300 BMW 535i --Lexus ES300
+ ... omitted several edges
$`#4`
IGRAPH 957a267 UNW- 8 11 --
+ attr: name (v/c), Type (v/x), community_id (v/x), degree (v/n), betweenness (v/n), hub_score (v/n), transitivity
| (v/n), top_car (v/c), weight (e/n)
+ edges from 957a267 (vertex names):
[1] Dodge Colt --Geo Storm Dodge Colt --Pontiac LeMans Dodge Colt --Subaru Loyale Dodge Colt --Suzuki Swift
[5] Dodge Colt --Toyota Tercel Ford Festiva --Subaru Justy Ford Festiva --Suzuki Swift Geo Storm --Pontiac LeMans
[9] Geo Storm --Subaru Loyale Pontiac LeMans--Subaru Loyale Suzuki Swift --Toyota Tercel
With functions neighbor_graph() and neighbor_attr(), we can extract
a the network of all neighbors of a given vertex and investigate the neighbors'
attributes.
Below, we were interested in neighbors of Audi 90:
audi90_neighbors <- neighbor_graph(car_network, name = 'Audi 90')
## names of the neighbors
> audi90_neighbors %>% V
+ 12/12 vertices, named, from cf07e58:
[1] Acura Legend Audi 90 Audi 100 Lexus ES300 Lexus SC300 Mazda MPV
[7] Mercedes-Benz 300E Mitsubishi Diamante Nissan Maxima Subaru Legacy Toyota Camry Volvo 850
## attributes of the neighbors including similarities (`weight`)
## with Audi 90
> neighbor_attr(car_network, name = 'Audi 90')
# A tibble: 12 × 5
index name Type community_id weight
<int> <chr> <fct> <fct> <dbl>
1 2 Acura Legend Midsize #2 0.939
2 3 Audi 90 Compact #2 NA
3 4 Audi 100 Midsize #2 0.936
4 45 Lexus ES300 Midsize #2 0.958
5 46 Lexus SC300 Midsize #2 0.909
6 52 Mazda MPV Van #2 0.904
7 55 Mercedes-Benz 300E Midsize #2 0.934
8 59 Mitsubishi Diamante Midsize #2 0.906
9 63 Nissan Maxima Midsize #2 0.912
10 78 Subaru Legacy Compact #1 0.921
11 82 Toyota Camry Midsize #1 0.905
12 88 Volvo 850 Midsize #1 0.964
Method summary() called for a graph/network object allows us to compute basic vertex
importance statistics:
-
degree: number of the vertex' neighbors
-
betweenness: numbers of the shortest paths between pairs of vertices which pass via the vertex of interest
-
hub score: eigenvector of the similarity matrix
-
transitivity: density of the neighborhood of the vertex
Below, we are computing these statistics for our car similarity network and setting them
as vertex attributes.
We also define a new attribute top_car, which stores names of cars with the largest
betweenness - these names will be later displayed in plots.
## vertex importance statistics
## labels for the cars with the highest betweenness and ignored for the rest
## the name labels will be shown in plots
car_stats <- car_network %>%
summary %>%
mutate(top_car = ifelse(betweenness > 200,
name, NA)) %>%
select(-index)
car_network <- car_network %>%
set_vertex_attributes(car_stats)
> get_vertex_attributes(car_network)
# A tibble: 88 × 9
index name Type community_id degree betweenness hub_score transitivity top_car
<int> <chr> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <chr>
1 1 Acura Integra Small #1 7 0 0.160 0.810 NA
2 2 Acura Legend Midsize #2 11 103 0.0474 0.527 NA
3 3 Audi 90 Compact #2 11 263 0.140 0.473 Audi 90
4 4 Audi 100 Midsize #2 7 43 0.0627 0.619 NA
5 5 BMW 535i Midsize #2 6 0 0.00996 0.667 NA
6 6 Buick Century Midsize #1 24 16 0.940 0.641 NA
7 7 Buick LeSabre Large #2 14 7 0.0139 0.670 NA
8 8 Buick Riviera Midsize #2 15 0 0.0168 0.714 NA
9 9 Cadillac DeVille Large #2 9 0 0.00568 0.917 NA
10 10 Cadillac Seville Midsize #2 5 5 0.000695 0.5 NA
# ℹ 78 more rows
# ℹ Use `print(n = ...)` to see more rows
Our graphExtra package overwrites the plot() method for igraph graphs/networks,
to generate plots in ggplot format, which can be easily customized by the user.
Under the hood, plot() makes use of tools of ggnetwork package.
This means, that it is always possible to add new node and edge symbols or labels to an
existing graph.
Below, we generate two plots of the car network with Fruchterman-Reingold algorithm.
In the first plot, the vertex symbol color codes for the community assignment; in the second one,
the vertex color codes for the betweenness statistic - aiming at identification of "hub cars".
The vertex symbol shape codes for car type.
By setting weighting_order = 3, we guarantee that the line width and alpha for the edges is proportional
to the third power of similarity statistics.
Consequently weighting_order = 0 specifies that all edges in the plot have the same width independently
of the similarity statistic.
The plots are styled with color, fill, shape, alpha and line width scales provided by the ggplot tool set:
## some plot globals
linewidth_range <- c(0.2, 1)
alpha_range <- c(0.2, 0.5)
type_shapes <- c(15:19, 9)
community_colors <- c("aquamarine4", "orangered3", "steelblue")
## community plot
car_network_plots <- list()
car_network_plots$community_id <-
plot(car_network,
layout = layout.fruchterman.reingold,
vertex_fill_variable = 'community_id',
vertex_shape_variable = 'Type',
vertex_label_variable = 'top_car',
vertex_txt_color_variable = 'community_id',
weighting_order = 3,
label_edges = FALSE,
label_vertices = TRUE,
seed = 12345,
plot_title = 'Cars93 network, communities',
box.padding = 0.5,
force = 2) +
scale_color_manual(values = community_colors) +
scale_fill_manual(values = community_colors)
## point color codes for betweennes
car_network_plots$betweennes <-
plot(car_network,
layout = layout.fruchterman.reingold,
vertex_fill_variable = 'betweenness',
vertex_shape_variable = 'Type',
vertex_label_variable = 'top_car',
vertex_txt_color_variable = 'betweenness',
weighting_order = 3,
label_edges = FALSE,
label_vertices = TRUE,
seed = 12345,
plot_title = 'Cars93 network, node betweenness',
box.padding = 0.5,
force = 2) +
scale_fill_gradient2(low = 'steelblue',
mid = 'black',
high = 'firebrick',
midpoint = 200,
limits = c(0, 400),
oob = scales::squish) +
scale_color_gradient2(low = 'steelblue',
mid = 'black',
high = 'firebrick',
midpoint = 200,
limits = c(0, 400),
oob = scales::squish)
## common styling
car_network_plots <- car_network_plots %>%
map(~.x +
scale_linewidth(range = linewidth_range) +
scale_alpha_continuous(range = alpha_range) +
scale_shape_manual(values = type_shapes))
car_network_plots$community_id +
car_network_plots$betweennes
As we can infer from the plots, the communities are expected to differ in car sizes, with community #1 enriched with small and compact cars, community #2 enriched with midsize, large and van vehicles, and community #2 consisting almost exclusively of small automobiles. With few lines of code, we can extract, quantify, and plot percentages of car types in the communities:
community_types <- car_network %>%
get_vertex_attributes %>%
group_by(community_id) %>%
count(Type) %>%
mutate(n_total = sum(n),
percent = n/n_total) %>%
ungroup
> community_types
# A tibble: 11 × 5
community_id Type n n_total percent
<fct> <fct> <int> <int> <dbl>
1 #1 Small 13 44 0.295
2 #1 Compact 15 44 0.341
3 #1 Midsize 7 44 0.159
4 #1 Sporty 9 44 0.205
5 #2 Compact 1 36 0.0278
6 #2 Midsize 15 36 0.417
7 #2 Large 8 36 0.222
8 #2 Van 8 36 0.222
9 #2 Sporty 4 36 0.111
10 #4 Small 7 8 0.875
11 #4 Sporty 1 8 0.125
community_type_plot <- community_types %>%
ggplot(aes(x = percent,
y = reorder(paste(community_id, n_total, sep = "\nn = "),
-as.integer(community_id)),
fill = Type)) +
geom_bar(stat = "identity",
position = position_stack(),
color = "black") +
scale_fill_brewer(palette = "Set2") +
theme_classic() +
labs(title = "Car types in the network communities",
x = "% of community",
y = "community, Leiden")
