Intermediate Network Analysis: Network Vizualization: Application (R)

### Load standardpackages
library(tidyverse) # Collection of all the good stuff like dplyr, ggplot2 ect.
library(magrittr) # For extra-piping operators (eg. %<>%)

library(tidygraph)
library(igraph)
library(ggraph)

This session

Welcome to your second part of the introduction to network analysis. In this session you will learn:

1. xxx

Introduction

• The main concern in designing a network visualization is the purpose it has to serve.
• What are the structural properties that we want to highlight? What are the key concerns we want to address?

• Network maps are far from the only visualization available for graphs - other network representation formats, and even simple charts of key characteristics, may be more appropriate in some cases.

• In network maps, as in other visualization formats, we have several key elements that control the outcome. The major ones are color, size, shape, and position.

Visualization Basics

# We load the highschool network nd make up som characteristics
set.seed(1337)
g <- as_tbl_graph(highschool, directed = TRUE) %E>%
  mutate(weight = sample(1:5, n(), replace = TRUE),
         year = year %>% as.factor()) %N>%
  mutate(class = sample(LETTERS[1:3], n(), replace = TRUE),
         gender = rbinom(n = n(), size = 1, prob = 0.5) %>% as.logical(),
         label = randomNames::randomNames(gender = gender, name.order = "first.last"))

set.seed(1337)
g <- g %N>%
  mutate(community = group_edge_betweenness(weights = weight, directed = TRUE) %>% as.factor()) %N>%
  filter(!node_is_isolated()) 

g <- g %N>%
  mutate(popular = case_when(
    centrality_degree(mode = 'in') < 5 ~ 'unpopular',
    centrality_degree(mode = 'in') >= 15 ~ 'popular',
    TRUE  ~ 'medium') %>% factor()
    )

g %N>%
  as_tibble() %>%
  head()

Node Visualization

• Nodes in a network are the entities that are connected. Sometimes these are also referred to as vertices.
• While the nodes in a graph are the abstract concepts of entities, and the layout is their physical placement, the node geoms are the visual manifestation of the entities.

Node positions

• Conceptually one can simply think of it in terms of a scatter plot — the layout provides the x and y coordinates, and these can be used to draw nodes in different ways in the plotting window.
• Actually, due to the design of ggraph the standard scatterplot-like geoms from ggplot2 can be used directly for plotting nodes:

set.seed(1337)
g %>%
  ggraph(layout = "nicely") + 
    geom_point(aes(x = x, y = y))

• The reason this works is that layouts (about which we talk in a moment) return a data.frame of node positions and metadata and this is used as the default plot data:

set.seed(1337)
g_layout <- g %>% create_layout(layout = "nicely") %>% select(x,y) 

g_layout %>% head()

• While usage of the default ggplot2 is theoreticlly fine, ggraph practically comes with its own set of node geoms (geom_node_*()).
• They by default already inherit the layout x and y coordinates, and come with extra features for network visualization.
• ggraph also comes with an own plotting theme (theme_graph()), which optimizes for graph visualization, and we might want to use.

g %>% ggraph(layout = g_layout) + 
  geom_node_point() +
  theme_graph()

• Usually (but not always) when visualizing a network, we are interested in the connectivity structure as expressed by the interplay between nodes and edges.
• So, lets also plot the edges (the geometries from the geom_edge_* family, about which we talk in a moment)

g %>% ggraph(layout = g_layout) + 
  geom_node_point() + 
  geom_edge_link(alpha = 0.25) +
  theme_graph()

Size

• Size is the first obvious choice to highlight important (eg. central) nodes on a contineous scale.

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_point(aes(size = centrality_degree())) +
  theme_graph()

Color

• Color can also be used to visualize importance in a second continuous dimension, or to highlight categorical features

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_point(aes(color = community)) +
  theme_graph()

Alpha

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_point(aes(alpha = centrality_degree())) +
  theme_graph()

Shapes

• In case we want to express even more categorical characteristics, we can also (just like in the visualiation of tabular data) use node shapes.

shapes() 

 [1] "circle"     "crectangle" "csquare"    "none"       "pie"        "raster"     "rectangle" 
 [8] "sphere"     "square"     "vrectangle"

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_point(aes(shape = gender)) +
  theme_graph() 

Labels

• With the geom_node_text geometry, we can also ad labels to the node. They are subject to common aestetics.

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_text(aes(label = label)) +
  theme_graph() 

In large graphs, plotting labels can appear messy, so it might make sense to only focus on important nodes to label

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_point() +
  geom_node_text(aes(label = label), repel = TRUE) +
  theme_graph() 

• Still looks like too much. If we want to highlight only certain important nodes with label, we can also only plot them.
• Note that (very practical) all ggraph geoms have a filter aestetic we can use for that

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_point() +
  geom_node_text(aes(label = label, 
                     filter = centrality_degree() >= centrality_degree()  %>% quantile(0.9)), 
                 repel = TRUE) +
  theme_graph() 

Combined node visualization tools

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(alpha = 0.25) +
  geom_node_point(aes(size = centrality_eigen(), 
                      color = community,
                      shape = gender)) +
  geom_node_text(aes(label = label, 
                     filter = centrality_eigen() >= centrality_eigen() %>% quantile(0.90)), 
                 repel = TRUE) +
  theme_graph() +
  theme(legend.position = 'none')

Edge Visualization

• So, now that we captured nodes, lets see how we can highlight aspects of edges, which are visualized with the geometries of the geom_edge_* family.

Weight

• Obviously, the edge weight (=thickness)

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(aes(width = weight), alpha = 0.25) +
  geom_node_point() +
  theme_graph() 

• Unfortunately, I wind the default to thick. We can also scale it.

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(aes(width = weight), alpha = 0.25) +
  scale_edge_width(range = c(0.1, 2)) + 
  geom_node_point() +
  theme_graph() 

Color

• Color can also be used to highlight edge significance (continuous)
• However, color is more often used to highlight different edge categories.
• Notice, since we want to represent the colors of potentially multiple edges between a node pair, I now use the geom_edge_fan geometry.

g %>% ggraph(layout = g_layout) + 
  geom_edge_fan(aes(size = weight,
                     color = year), alpha = 0.25) +
  geom_node_point() +
  theme_graph() 

Density

• Density plots can also be used to highlight densely connected regions.

g %>% ggraph(layout = g_layout) + 
  geom_edge_link(aes(col = year), alpha = 0.1) +
  geom_edge_density(aes(fill = year)) +
  geom_node_point() +
  theme_graph() 

Directionality

• The easiest way to express directionality is by defining the arrow(), which comes with own aestetics.

g %>% ggraph(layout = g_layout) + 
  geom_edge_fan(aes(color = year), 
                arrow = arrow(),
                alpha = 0.5) +
  geom_node_point() +
  theme_graph() 

• The default open arrow and other settings are a bit ugly, so we use some adittional aestetics

g %>% ggraph(layout = g_layout) + 
  geom_edge_fan(aes(color = year), 
                arrow = arrow(type = "closed", length = unit(2, "mm")),
                start_cap = circle(1, "mm"),
                end_cap = circle(1, "mm"),
                alpha = 0.5) +
  geom_node_point() +
  theme_graph() 

• Another nice trick is to work with alphas or colors, which change between start and end node.

g %>%
  ggraph(layout = g_layout) + 
  geom_edge_fan(aes(color = year,
                    alpha = stat(index)) # Notice that
                ) +
  geom_node_point() +
  theme_graph() + 
  scale_edge_alpha("Edge direction", guide = "edge_direction")

• It can also be really practical to change edge characteristics by the characteristics of their adjacent nodes.
• Remember, with .N(), we can access them to do so.

set.seed(1337)
g %>%
  ggraph(layout = 'nicely') + 
  geom_edge_fan(aes(color = .N()$community[to]), # Notice that
                alpha = 0.5,
                show.legend = FALSE) +
  geom_node_point(aes(color = community),
                  show.legend = FALSE) +
  theme_graph() 

Layouts

• The graph layout refers to the node position on the reference system.

Ordinary graph style

• Graphs can be represented in simple geometries such as squares, circles, lines, or randomly.
• Or, specialized algorithms can be used to position nodes according to the properties of their connectivity.
• They are usually designed to highlight different aspects of the network.
• Lets inspect some standard layouts

set.seed(1337)
library(ggpubr)
layout_list <- c("randomly", "linear", "circle", 
                 "grid", "fr", "kk", 
                 "graphopt", "stress", 'mds', 
                 'dh', 'drl', 'lgl')

g_list <- list(NULL)
for(i in 1:length(layout_list)){
  g_list[[i]] <-g %>% 
    ggraph(layout = layout_list[i]) + 
  geom_edge_fan(aes(color = year,
                    width = weight,
                    alpha = weight), 
                arrow = arrow(type = "closed", length = unit(2, "mm")),
                start_cap = circle(1, "mm"),
                end_cap = circle(1, "mm"),
                show.legend = FALSE) +
    scale_edge_width(range = c(0.1, 0.5)) + 
    geom_node_point(aes(size = centrality_degree(mode = 'in'), 
                        color = community,
                        shape = gender),
                    show.legend = FALSE) +
    theme_graph() +
    labs(title = paste("Layout:", layout_list[i], sep = " "))
}

ggarrange(plotlist = g_list, nrow = 4, ncol = 3)

Arcs and circles

# An arc diagram
g %>% ggraph(layout = 'linear') + 
  geom_edge_arc() +
  geom_node_point(aes(size = centrality_degree(), 
                      color = community),
                  show.legend = FALSE) +
    theme_graph() 

# An arc diagram
g %>% ggraph(layout = 'linear', circular = TRUE) + 
  geom_edge_arc(aes(color = .N()$community[to])) +
  geom_node_point(aes(size = centrality_degree(), 
                      color = community),
                  show.legend = FALSE) +
    theme_graph() +
  coord_fixed()

Hive plots

• A hive plot, while still technically a node-edge diagram, is a bit different from the rest as it uses information pertaining to the nodes, rather than the connection information in the graph.
• This means that hive plots, to a certain extent are more interpretable as well as less vulnerable to small changes in the graph structure.
• They are less common though, so use will often require some additional explanation.

g %>%
  ggraph(layout = 'hive', axis = popular, sort.by = centrality_degree(mode = 'in')) + 
    geom_edge_hive(aes(colour = year, alpha = ..index..), show.legend = FALSE) + 
    geom_axis_hive(aes(colour = popular), size = 3, label = FALSE) + 
    coord_fixed() + 
  theme_graph() +
  theme(legend.position = 'bottom')

Social Fabric

g %>% ggraph(layout = 'fabric', sort.by = community) + 
  geom_node_range(aes(colour = community), alpha = 0.3) + 
  geom_edge_span(aes(col = .N()$community[to]), end_shape = 'circle', alpha = 0.5) + 
  coord_fixed() + 
  theme_graph() +
  theme(legend.position = 'none')

Visualizing Hirarchical networks

• If the network is by definition hierarchical, edges can only exist between nodes of higher to lower dept (eg. tree structures).

• This offers us possibility for quite some adittional ways of representing it which are geared towards hirarchical (=nested) structures

• Here an example of the dependency structures of the flare package

edges <- flare$edges
vertices <- flare$vertices %>% arrange(name) %>% mutate(name=factor(name, name))
connections <- flare$imports

vertices %>% head()

edges %>% head()

connections %>% head()

g_hir <- tbl_graph(vertices, edges)

g_hir

Tree structures

g_hir %>% ggraph('tree') + 
  geom_edge_diagonal() +
  theme_graph()

g_hir %>% ggraph( 'dendrogram') + 
    geom_edge_elbow() +
  theme_graph()

g_hir %>% ggraph('dendrogram', circular = TRUE) + 
    geom_edge_elbow() + 
    coord_fixed() +
  theme_graph()

# The connection object must refer to the ids of the leaves:
from = match(connections$from, vertices$name)
to = match(connections$to, vertices$name)

g_hir %>% ggraph(layout = 'dendrogram', circular = TRUE) + 
  geom_conn_bundle(data = get_con(from = from, to = to), alpha = 0.1) + 
  geom_edge_diagonal0() +
  #geom_node_text(aes(filter = leaf, angle = node_angle(x, y), label = shortName),
  # hjust = 'outward', size = 2) +
  coord_fixed() +
  theme_graph()

Non-edge-based

# An icicle plot
g_hir %>% ggraph('partition') + 
  geom_node_tile(aes(fill = depth), size = 0.25) +
  theme_graph()

# A sunburst plot
g_hir %>% ggraph('partition', circular = TRUE) + 
  geom_node_arc_bar(aes(fill = depth), size = 0.25) + 
  coord_fixed() +
  theme_graph()

g_hir %>% ggraph('circlepack') + # , weight = size
  geom_node_circle(aes(fill = depth), size = 0.25, n = 50) + 
  coord_fixed() +
  theme_graph()

g_hir %>% ggraph('treemap') + 
  geom_node_tile(aes(fill = depth), size = 0.25) +
  theme_graph()

Geospatial networks

Defining a map

library(maps)

map_us <- map_data("usa")

map_us %>%
  head()

Getting some network data

library(anyflights)

us_airports <- get_airports() %>%
  filter(lat >= 24 & lat <= 49 & lon >= -124 & lon <= -66)  %>%
  rename(name_full = name,
         name = faa)

us_airports %>% head()

flights <- get_flights(station = us_airports %>% pull(name), year = 2015, month = 5)

flights %>% head()

edges <- flights %>% count(origin, dest, sort = TRUE) %>%
  rename(from = origin, to = dest, weight = n) %>%
  semi_join(us_airports, by = c('from' = 'name')) %>%
  semi_join(us_airports, by = c('to' = 'name')) %>% 
  filter(percent_rank(weight) >= 0.25)

g_geo <- tbl_graph(nodes = us_airports, edges = edges, directed = TRUE) %N>%
  filter(!node_is_isolated())

Constructing a graph

coords <- g_geo %N>% 
  as_tibble() %>% 
  select(lat, lon) %>%
  rename(x = lon, y = lat)

g_geo %>%
  ggraph(layout = coords) +
  geom_polygon(data = map_us, aes(x=long, y = lat, group = group), fill = "#CECECE", color = "#515151") + 
  geom_edge_arc(aes(width = weight,   
                    alpha = weight,
                    filter = percent_rank(weight) >= 0.75,
                    circular = FALSE),
                strength = 0.33,
                color = 'chocolate2') +
  geom_node_point(aes(size = centrality_degree(),
                      col = centrality_degree())) + 
  scale_edge_width_continuous(range = c(0.1, 1)) + 
  coord_fixed(1.3) + 
  theme_graph() + 
  theme(legend.position = 'none')

Interactive networks

• There are numerous ways to to interactive network visualizations in R
• For the sake of time, I just show you what I find the easiest and most consistent implementation (plotly unfortunately does by now not support ggraph)

library(ggiraph)

g_plot_int <- g %>% 
  ggraph(layout = layout_list[i]) + 
  geom_edge_fan(aes(color = year,
                    width = weight,
                    alpha = weight), 
                arrow = arrow(type = "closed", length = unit(2, "mm")),
                start_cap = circle(1, "mm"),
                end_cap = circle(1, "mm"),
                show.legend = FALSE) +
    scale_edge_width(range = c(0.1, 0.5)) + 
    geom_node_point(aes(size = centrality_degree(mode = 'in'), 
                        color = community,
                        shape = gender),
                    show.legend = FALSE) +
  geom_point_interactive(aes(x, y, # Notice this extra layer
                             tooltip = label, data_id = name, 
                             size = centrality_degree(mode = 'in')), alpha = 0.01) +  
    theme_graph() +
  theme(legend.position = 'none')

girafe(ggobj = g_plot_int, width_svg = 10, height_svg = 10) %>% 
    girafe_options(opts_zoom(max = 10), opts_tooltip(opacity = 0.7) )

Your turn

Please do Exercise 1 in the corresponding section on Github. This time you are about to do your own bibliographic analysis!

Endnotes

More info

Packages & Ecosystem

• tidygraph here
• ggraph here
• ggiraph here

Other souces

• Intro: Network Visualizations in R using ggraph and graphlayouts: Good intros to ggraph functionality & finetuning.
• Katherine Ognyanova’s Blog): Her blog is full of some of the most complete introductions to network visualization. Does use igraph, but there are for sure 1 or tricks you can learn from her, particularly when it’s about interactive network viosualization.
• Good slidedeck on static / interactive network viz in R: Worth visiting

Session info

sessionInfo()

R version 4.0.2 (2020-06-22)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.7

Matrix products: default
BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] gdtools_0.2.2    ggiraph_0.7.8    anyflights_0.3.0 maps_3.3.0       ggpubr_0.4.0    
 [6] ggraph_2.0.3     igraph_1.2.5     tidygraph_1.2.0  magrittr_1.5     forcats_0.5.0   
[11] stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4      readr_1.3.1      tidyr_1.1.2     
[16] tibble_3.0.3     ggplot2_3.3.2    tidyverse_1.3.0  knitr_1.30      

loaded via a namespace (and not attached):
 [1] fs_1.5.0            bit64_4.0.5         lubridate_1.7.9     progress_1.2.2     
 [5] httr_1.4.2          tools_4.0.2         backports_1.1.10    utf8_1.1.4         
 [9] R6_2.4.1            DBI_1.1.0           colorspace_1.4-1    withr_2.3.0        
[13] prettyunits_1.1.1   tidyselect_1.1.0    gridExtra_2.3       bit_4.0.4          
[17] curl_4.3            compiler_4.0.2      cli_2.0.2           rvest_0.3.6        
[21] pacman_0.5.1        randomNames_1.4-0.0 xml2_1.3.2          labeling_0.3       
[25] scales_1.1.1        systemfonts_0.3.2   digest_0.6.25       foreign_0.8-80     
[29] rmarkdown_2.4       rio_0.5.16          pkgconfig_2.0.3     htmltools_0.5.0    
[33] dbplyr_1.4.4        htmlwidgets_1.5.1   rlang_0.4.7         readxl_1.3.1       
[37] rstudioapi_0.11     farver_2.0.3        generics_0.0.2      jsonlite_1.7.1     
[41] vroom_1.3.2         zip_2.1.1           car_3.0-10          Rcpp_1.0.5         
[45] munsell_0.5.0       fansi_0.4.1         abind_1.4-5         viridis_0.5.1      
[49] lifecycle_0.2.0     stringi_1.5.3       yaml_2.2.1          carData_3.0-4      
[53] MASS_7.3-53         grid_4.0.2          blob_1.2.1          parallel_4.0.2     
[57] ggrepel_0.8.2       crayon_1.3.4        cowplot_1.1.0       graphlayouts_0.7.0 
[61] haven_2.3.1         hms_0.5.3           pillar_1.4.6        uuid_0.1-4         
[65] ggsignif_0.6.0      reprex_0.3.0        glue_1.4.2          evaluate_0.14      
[69] data.table_1.13.0   modelr_0.1.8        vctrs_0.3.4         tweenr_1.0.1       
[73] testthat_2.3.2      cellranger_1.1.0    gtable_0.3.0        polyclip_1.10-0    
[77] assertthat_0.2.1    xfun_0.18           ggforce_0.3.2       openxlsx_4.2.2     
[81] broom_0.7.1         rstatix_0.6.0       rsconnect_0.8.16    viridisLite_0.3.0  
[85] toOrdinal_1.1-0.0   ellipsis_0.3.1