Network Visualization I

Social Network Analysis

Termeh Shafie

A brief history of network visualization

Württemberg family tree (1585)

Bridges of Königsberg, Euler (1741)

Moreno (1934)

“Social Atom” representation Lundberg Steel (1938)

Davis et al (1941)

Loomis (1948)

First Graders Northway (1952)

Klovdahl’s (1982) adaptation of biology imaging software for social networks (ORTEP)

Vaseline - Prescribe the nation

Firework or network?

Visualizing “ordinary” data

	mpg	cyl	disp	hp	drat
Mazda RX4	21.0	6	160	110	3.90
Mazda RX4 Wag	21.0	6	160	110	3.90
Datsun 710	22.8	4	108	93	3.85
Hornet 4 Drive	21.4	6	258	110	3.08
Hornet Sportabout	18.7	8	360	175	3.15
Valiant	18.1	6	225	105	2.76

A scatterplot of the variables mpg and disp from the mtcars dataset

Visualizing “ordinary” data

	mpg	cyl	disp	hp	drat
Mazda RX4	21.0	6	160	110	3.90
Mazda RX4 Wag	21.0	6	160	110	3.90
Datsun 710	22.8	4	108	93	3.85
Hornet 4 Drive	21.4	6	258	110	3.08
Hornet Sportabout	18.7	8	360	175	3.15
Valiant	18.1	6	225	105	2.76

A scatterplot of the variables mpg and disp from the mtcars dataset. Dots are colored according to the variable cyl.

Visualizing “ordinary” data

	mpg	cyl	disp	hp	drat
Mazda RX4	21.0	6	160	110	3.90
Mazda RX4 Wag	21.0	6	160	110	3.90
Datsun 710	22.8	4	108	93	3.85
Hornet 4 Drive	21.4	6	258	110	3.08
Hornet Sportabout	18.7	8	360	175	3.15
Valiant	18.1	6	225	105	2.76

A scatterplot of the variables mpg and disp from the mtcars dataset. Dots are colored according to the variable cyl and the size is proportional to hp.

Visualizing “ordinary” data

	mpg	cyl	disp	hp	drat
Mazda RX4	21.0	6	160	110	3.90
Mazda RX4 Wag	21.0	6	160	110	3.90
Datsun 710	22.8	4	108	93	3.85
Hornet 4 Drive	21.4	6	258	110	3.08
Hornet Sportabout	18.7	8	360	175	3.15
Valiant	18.1	6	225	105	2.76

A boxplot of the variable drat grouped by cyl from the mtcars dataset

Visualizing networks is hard(er)

ordinary data

clear data format (rows: observations, columns: variables)
plot style dependent on variable scale (barchart, scatterplot, boxplot,…)
illustrate relations between variables
given relative positions

network data

different data formats (adjacency matrix, edgelist, adjaceny list, …)
how to choose a proper layout algorithm?
more degrees of freedom
can we draw any conclusions from a network plot?

network visualization tools

gephi
works quite well for visualizing large networks

visone
well designed GUI and algorithms
(graphlayouts implements most algorithms from it)

and many more
cytoscape, NodeXL, GraphViz, python, …

Network visualization in

which package(s) to choose?

igraph: great for analyses, but plotting can be tricky
(check out https://kateto.net/network-visualization)
networks as ggplot2 objects: ggnet2, ggnetwork
ggraph: grammar of graphics for networks
interactive/3D: visNetwork, threejs

why ggraph?

maintained by RStudio/Posit
stable and reliable (many other packages have been abandoned)
plays well with other packages

thoughtful API
extension of ggplot2
grammar of graphics

Grammar of graphics

Framework which follows a layered approach to describe and construct visualizations or graphics in a structured manner

Data: Always start with the data, identify the dimensions you want to visualize.

Aesthetics: Confirm the axes based on the data dimensions, positions of various data points in the plot. Also check if any form of encoding is needed including size, shape, color and so on which are useful for plotting multiple data dimensions.

Scale: Do we need to scale the potential values, use a specific scale to represent multiple values or a range?

Geometric objects: These are popularly known as ‘geoms’. This would cover the way we would depict the data points on the visualization. Should it be points, bars, lines and so on?

Statistics: Do we need to show some statistical measures in the visualization like measures of central tendency, spread, confidence intervals?

Facets: Do we need to create subplots based on specific data dimensions? Coordinate system: What kind of a coordinate system should the visualization be based on — should it be cartesian or polar?

Grammar of graphics

Data: Identify dimensions you want to visualize

Aesthetics/scales: Axes of data. Also size, shape, color, …

Geometries: depiction of data points (points, bars, lines, …)

Facets: Subplots based on specific dimensions?

Statistics: Show some statistical measures?

Coordinates: Type of coordinate system (cartesian, polar,…)

Theme: bling bling

Grammar of graphics (network edition)

Data: Identify dimensions you want to visualize

Aesthetics/scales: Axes of data. Also size, shape, color, …

Geometries: depiction of data points (points, bars, lines, …)

Facets: Subplots based on specific dimensions?

Statistics: Show some statistical measures?

Coordinates: Type of coordinate system (cartesian, polar,…)

Theme: bling bling

network data: the graph?

network data: data frames!

Nodes
name	sex	homeworld	species
R2-D2	none	Naboo	Droid
NUTE GUNRAY	male	Cato Neimoidia	Neimodian
OBI-WAN	male	Stewjon	Human
EMPEROR	male	Naboo	Human
JAR JAR	male	Naboo	Gungan
TARPALS	male	Naboo	Gungan

Edges
from	to	weight
WATTO	C-3PO	1
ANAKIN	GREEDO	1
EMPEROR	BAIL ORGANA	1
QUI-GON	GREEDO	1
JAR JAR	SEBULBA	2
OBI-WAN	BOSS NASS	2

+layout

see tidygraph

first full example (don’t panic!)

# load and manipulate data
data("starwars")
sw1 <- starwars[[1]]
sw_palette <- c("#1A5878", "#C44237", "#AD8941", "#E99093", "#50594B")
V(sw1)$interactions <- graph.strength(sw1) 

#plot
ggraph(graph = sw1,layout = "stress") + 
  geom_edge_link0(edge_colour = "grey25",
                  aes(edge_linewidth = weight)) +
  geom_node_point(shape = 21, color = "black",stroke = 1,
                  aes(fill = sex,size = interactions)) +
  geom_node_text(color = "black", size = 4, repel = FALSE, 
                 aes(filter = (interactions>=65),label = name))+
  scale_edge_width(range = c(0.1,1.5),guide = "none")+
  scale_size(range = c(3,10),guide = "none")+
  scale_fill_manual(values = sw_palette, na.value = "grey",name = "")+
  coord_fixed()+
  theme_graph() +
  theme(legend.position = "bottom") +
  guides(fill = guide_legend(override.aes = list(size=6)))

first full example (don’t panic!)

1) layout

ggraph(graph = sw1,layout = "stress", ...)

graph: igraph object sw1 (can also be a tidygraph object)
layout: used algorithm
…: additional parameters depend on algorithm

Graph drawing

Criteria for “pleasing” layouts:

minimising edge crossings
minimising edge bends
maximising symmetry
maximising the minimum angle between edges leaving a node
maximising node/edge orthogonality

Matrix representation

Sometimes we do not need a node-edge diagram

g <- sample_islands(2,10,0.8,3)
ggraph(g,"matrix")+
  geom_edge_point(mirror = TRUE)

Matrix representation

But it can be tricky to find an adequate ordering

g <- permute(g,sample(1:20))
ggraph(g,"matrix")+
  geom_edge_point(mirror = TRUE)

Matrix representation

If one is known, it can be supplied as an argument

ord <- membership(cluster_leading_eigen(g))
ggraph(g,"matrix",sort.by = ord)+
  geom_edge_point(mirror = TRUE)

Matrix representation

The seriation package has a nicer out of the box method

A <- as_adj(g, sparse = FALSE)
ser <- order(ord)
seriation::ggpimage(A[ser,ser])+theme(legend.position = "none")

2) edges: geoms

geom_edge_link0(edge_colour = "grey25", aes(edge_linewidth = weight))

ls("package:ggraph",pattern = "geom_edge_*")
#>  [1] "geom_edge_arc"             "geom_edge_arc0"           
#>  [3] "geom_edge_arc2"            "geom_edge_bend"           
#>  [5] "geom_edge_bend0"           "geom_edge_bend2"          
#>  [7] "geom_edge_bundle_force"    "geom_edge_bundle_force0"  
#>  [9] "geom_edge_bundle_force2"   "geom_edge_bundle_minimal" 
#> [11] "geom_edge_bundle_minimal0" "geom_edge_bundle_minimal2"
#> [13] "geom_edge_bundle_path"     "geom_edge_bundle_path0"   
#> [15] "geom_edge_bundle_path2"    "geom_edge_density"        
#> [17] "geom_edge_diagonal"        "geom_edge_diagonal0"      
#> [19] "geom_edge_diagonal2"       "geom_edge_elbow"          
#> [21] "geom_edge_elbow0"          "geom_edge_elbow2"         
#> [23] "geom_edge_fan"             "geom_edge_fan0"           
#> [25] "geom_edge_fan2"            "geom_edge_hive"           
#> [27] "geom_edge_hive0"           "geom_edge_hive2"          
#> [29] "geom_edge_link"            "geom_edge_link0"          
#> [31] "geom_edge_link2"           "geom_edge_loop"           
#> [33] "geom_edge_loop0"           "geom_edge_parallel"       
#> [35] "geom_edge_parallel0"       "geom_edge_parallel2"      
#> [37] "geom_edge_point"           "geom_edge_sf"             
#> [39] "geom_edge_span"            "geom_edge_span0"          
#> [41] "geom_edge_span2"           "geom_edge_tile"

geom_edge_type: generate n points, draw path
geom_edge_type0: direct line
geom_edge_type2: can interpolate node parameters

2) edges: geoms

geom_edge_link0(edge_colour = "grey25", aes(edge_linewidth = weight))

ls("package:ggraph",pattern = "geom_edge_*")
#>  [1] "geom_edge_arc"             "geom_edge_arc0"           
#>  [3] "geom_edge_arc2"            "geom_edge_bend"           
#>  [5] "geom_edge_bend0"           "geom_edge_bend2"          
#>  [7] "geom_edge_bundle_force"    "geom_edge_bundle_force0"  
#>  [9] "geom_edge_bundle_force2"   "geom_edge_bundle_minimal" 
#> [11] "geom_edge_bundle_minimal0" "geom_edge_bundle_minimal2"
#> [13] "geom_edge_bundle_path"     "geom_edge_bundle_path0"   
#> [15] "geom_edge_bundle_path2"    "geom_edge_density"        
#> [17] "geom_edge_diagonal"        "geom_edge_diagonal0"      
#> [19] "geom_edge_diagonal2"       "geom_edge_elbow"          
#> [21] "geom_edge_elbow0"          "geom_edge_elbow2"         
#> [23] "geom_edge_fan"             "geom_edge_fan0"           
#> [25] "geom_edge_fan2"            "geom_edge_hive"           
#> [27] "geom_edge_hive0"           "geom_edge_hive2"          
#> [29] "geom_edge_link"            "geom_edge_link0"          
#> [31] "geom_edge_link2"           "geom_edge_loop"           
#> [33] "geom_edge_loop0"           "geom_edge_parallel"       
#> [35] "geom_edge_parallel0"       "geom_edge_parallel2"      
#> [37] "geom_edge_point"           "geom_edge_sf"             
#> [39] "geom_edge_span"            "geom_edge_span0"          
#> [41] "geom_edge_span2"           "geom_edge_tile"

geom_edge_link0() and geom_edge_parallel0() suffice

2) edges: geom type examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3) 
V(g)$type <- c("a", "b", "c")

ggraph(g, "stress") +
  geom_edge_link(edge_linewidth = 2, aes(color = stat(index)))

2) edges: geom type examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3) 
V(g)$type <- c("a", "b", "c")

ggraph(g, "stress") +
  geom_edge_link(edge_linewidth = 2, aes(color = stat(index)), n = 3)

2) edges: geom type examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3)
V(g)$type <- c("a", "b", "c")

ggraph(g, "stress") +
  geom_edge_link2(edge_linewidth = 2, aes(color = node.type))

2) edges: geom type examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3)
V(g)$type <- c("a", "b", "c")

ggraph(g, "stress") +
  geom_edge_link2(edge_linewidth = 2, aes(color = node.type), n = 3)

2) edges: geom type examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3)
V(g)$type <- c("a", "b", "c")

ggraph(g, "stress") +
  geom_edge_link0(edge_linewidth = 2)

2) edges: geom type examples

# add another edge between nodes one and two to obtain a multi edge.
g <- add.edges(g, c(1,2))


ggraph(g, "stress") +
  geom_edge_parallel0(edge_linewidth = 0.5)

2) edges: aesthetics

geom_edge_link0(edge_colour = "grey25", aes(edge_linewidth = weight))

mapping aesthetics

global: all edges have the same appearance
(e.g. edge_colour = "grey25")
via attributes: appearance depends on attribute
(e.g. aes(edge_linewidth = weight))

available aesthetics
edge_colo(u)r, edge_linewidth, edge_linetype, edge_alpha

2) edges: aesthetics examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3) 
E(g)$weight <- c(1, 2, 0.5)

ggraph(g, "stress") +
  geom_edge_link0(edge_linetype = "dotted")

2) edges: aesthetics examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3) 
E(g)$weight <- c(1, 2, 0.5)

ggraph(g, "stress") +
  geom_edge_link0(edge_alpha = 0.5)

2) edges: aesthetics examples

# create a simple graph of three nodes where all nodes are connected
g <- graph.full(3) 
E(g)$weight <- c(1, 2, 0.5)

ggraph(g, "stress") +
  geom_edge_link0(aes(edge_alpha = weight, edge_linewidth = weight))

2) edges: misc

g <- graph.full(3,directed = TRUE)

ggraph(g, "stress") +
  geom_edge_parallel0(edge_linewidth = 0.5,
    arrow = arrow(angle = 15, length = unit(0.15, "inches"),
                  ends = "last", type = "closed"))

3) nodes: geoms

geom_node_point(shape = 21, color = "black",stroke = 1, aes(fill = sex,size = interactions))

ls("package:ggraph",pattern = "geom_node_*")
#> [1] "geom_node_arc_bar" "geom_node_circle"  "geom_node_label"  
#> [4] "geom_node_point"   "geom_node_range"   "geom_node_sf"     
#> [7] "geom_node_text"    "geom_node_tile"    "geom_node_voronoi"

geom_node_point(): draw nodes as a simple point

3) nodes: aesthetics

geom_node_point(shape = 21, color = "black",stroke = 1, aes(fill = sex,size = interactions))

mapping aesthetics

global: all nodes have the same appearance
(e.g. shape = 21)
via attributes: appearance depends on attribute
(e.g. aes(fill = sex))

available aesthetics
alpha, colo(u)r, fill, shape, size, stroke
(usage of colour, fill, and stroke depend on shape)

3) nodes: aesthetic examples

g <- graph.full(3)

ggraph(g, "stress") +
  geom_edge_link0() +
  geom_node_point(size = 5, color = "red")

3) nodes: aesthetic examples

g <- graph.full(3)

ggraph(g, "stress") +
  geom_edge_link0() +
  geom_node_point(size = 5, shape = 21, color = "red", fill = "black", stroke = 2)

3) nodes: aesthetic examples

g <- graph.full(3)

ggraph(g, "stress") +
  geom_edge_link0() +
  geom_node_point(size = 5, shape = 22, color = "red", fill = "black", stroke = 2)

4) labels: geoms

geom_node_text(color = "grey25", size = 4, repel = FALSE, aes(filter = (interactions>=65),label = name))

geom_node_text(): add text to node
geom_node_label(): add text to node with frame

geom_node_text is the preferred choice

4) labels: aesthetics

geom_node_text(color = "grey25", size = 4, repel = FALSE, aes(filter = (interactions>=65),label = name))

mapping aesthetics
- global: specify font properties
- via attributes: set label to name attribute of node
- filter: only display for nodes (or edges!) that fulfil a given criterion

available aesthetics
many! but most important: label, colour, family, size, and repel

4) labels: aesthetics examples

g <- graph.full(3)
V(g)$name <- c("A", "B", "C")

ggraph(g, "stress") +
  geom_edge_link0() +
  geom_node_point(size = 5, color = "grey66")+
  geom_node_text(aes(label = name), color = "black") + coord_fixed(clip = "off")

4) labels: aesthetics examples

g <- graph.full(3)
V(g)$name <- c("A", "B", "C")

ggraph(g, "stress") +
  geom_edge_link0() +
  geom_node_point(size = 5, color = "grey66")+
  geom_node_label(aes(label = name), color = "black") + coord_fixed(clip = "off")

5) scales

scale_edge_width(range = c(0.1,1.5),guide = "none")
scale_size(range = c(3,10),guide = "none")
scale_fill_manual(values = sw_palette, na.value = "grey",name = "")

control aesthetics that are mapped within aes()
although optional, set one scale_* per parameter in any aes()

form of scale functions
scale_<aes>_<variable type>()

additional options
guide (show legend or not), name (label in legend), na.value (value for NAs)

5) scales: variable types

node size and edge width (and node/edge alpha)
scale_size() and scale_edge_width()
most relevant parameter is range = c(min,max)

continuous variable to colour
scale_(edge_)colour_gradient(low = ...,high = ...)

categorical variable to colour
scale_colour_brewer()
scale_colour_manual(values = ...)

misc: scale_shape() and scale_edge_linetype()

5) scales: examples

ggraph(graph = sw1,layout = "stress") + 
  geom_edge_link0(aes(edge_linewidth = weight)) +
  geom_node_point(size = 5, shape = 21, aes(fill = sex)) +
  scale_edge_width(range = c(0.1,1.5),guide = "none")+
  scale_fill_manual(values = sw_palette, na.value = "grey",name = "")+
  theme(legend.position = "bottom")

5) scales: examples

ggraph(graph = sw1,layout = "stress") + 
  geom_edge_link0(aes(edge_linewidth = weight), show.legend = FALSE) +
  geom_node_point(size = 5, shape = 21, aes(fill = sex)) +
  theme(legend.position = "bottom")

5) scales: examples

ggraph(graph = sw1,layout = "stress") + 
  geom_edge_link0(aes(edge_linewidth = weight)) +
  geom_node_point(size = 5, shape = 21, aes(fill = sex)) +
  scale_edge_width(range = c(0.1,1.5),guide = "none")+
  scale_fill_brewer(palette = "Set1", na.value = "grey",name = "")+
  theme(legend.position = "bottom")

5) scales: examples

ggraph(graph = sw1,layout = "stress") + 
  geom_edge_link0(aes(edge_linewidth = weight)) +
  geom_node_point(size = 5, fill = "grey25", aes(shape = sex)) +
  scale_edge_width(range = c(0.1,1.5),guide = "none")+
  scale_shape_manual(values=21:24, na.value = 25,name = "")+
  theme(legend.position = "bottom")

6) themes

theme_graph() + theme(legend.position = "bottom")

control the overall look of the plot

theme() has a lot of options but we really don’t need them (except legend.position)
theme_graph() erases all defaults (e.g. axis, grids, etc.)

guides(fill = guide_legend(override.aes = list(size=6)))

change appearance of geoms in legend (highly optional!)

summary

layout
ggraph(graph,layout = "stress") +

edges
geom_edge_link0(<<global>>,aes(<<via variables>>)) +

nodes
geom_node_point(<global>,aes(<via variables>)) +
geom_node_text(<global>,aes(<via variables>)) +

scales
scale_<aes>_<variable type>() + (one per variable in aes())

themes
theme_graph()

first full example (revisited)

ggraph(graph = sw1,layout = "stress") + 
  geom_edge_link0(edge_colour = "grey25",
                  aes(edge_linewidth = weight)) +
  geom_node_point(shape = 21, color = "black",stroke = 1,
                  aes(fill = sex,size = interactions)) +
  geom_node_text(color = "black", size = 4, repel = FALSE, 
                 aes(filter = (interactions>=65),label = name))+
  scale_edge_width(range = c(0.1,1.5),guide = "none")+
  scale_size(range = c(3,10),guide = "none")+
  scale_fill_manual(values = sw_palette, na.value = "grey",name = "")+
  coord_fixed()+
  theme_graph() +
  theme(legend.position = "bottom") +
  guides(fill = guide_legend(override.aes = list(size = 6)))

Next time

graph layouts
dynamic visualization
interactive visualization
enhancing visualizations