Network Visualizations

Kevin Reuning

Data for Today

We are going to use two networks today:

• A network of workers involved in a strike: strike.paj You can find more info here
• Network of Ohio interest groups. The edge data is here, the nodal data is here.
• Network of high school relationships. The edge data is here, the nodal data is here.

The worker data is in the a “pajek” format:

net <- read_graph("strike.paj", format="pajek")

The other two can be loaded by combining the edge and nodes:

oh_edges <- read.csv("data/edge_OH.csv")
oh_nodes <- read.csv("data/meta_OH.csv")
oh_net <- graph_from_data_frame(oh_edges, vertices=oh_nodes, directed=F)

Goals for this Session

• Make (useful) network visualizations.
• Talk about different network layout algorithms.

Visualizing Networks

Now we are going to move onto visualizing networks.

Visualizations can be useful with network data, but they are also hard to do:

• We have complicated data.
• We often want to show multiple “types” of information.

Package

We are going to use the ggraph package.

Benefits:

• It uses a ggplot2 style interface.
• It allows a lot of fine-tuning of plots.
• Has a fair amount of useful online documentation on layouts, nodes, and edges

Cons:

• It is a bit overly complicated at times.

New Data

We are going to start with a small canned dataset you can download from the internet: strike.paj

It is a communication network between workers at a sawmill. It also is a unique data format: “pajek” which thankfully igraph has a function for

library(igraph)
net <- read_graph("data/strike.paj", format="pajek")
ecount(net)

[1] 38

vcount(net)

[1] 24

Basics of Plot

Just like ggplot2 all visualizations will start with a call to ggraph()

library(ggraph)
ggraph(net)

Adding Nodes and Edges

To add nodes and edges to this plot we will use geom_node_point() and geom_edge_link()

• geom_node_point: Adds our nodes as circles
• geom_edge_link: Adds edges as straight lines (no arrows)

ggraph(net) + geom_node_point(size=6) +
    geom_edge_link()

Color, Scale, etc

We can change the visuals of edges and nodes by assigning:

• color= Color of edge or node
• size= Size of the nodes (defaults to 1)
• width= The width of the edges (defaults to .5 (I think))
• alpha= The amount of transparency for nodes or edges.

ggraph(graph=net) + 
  geom_edge_link(color="gray") +    
  geom_node_point(color="skyblue3", size=5)

Ordering

The order of what you add on matters with later things being added on top of earlier things.

p1 <- ggraph(graph=net) + 
  geom_edge_link(width=2) +    
  geom_node_point(color="skyblue3", size=8)
p2 <- ggraph(graph=net) + 
  geom_node_point(color="skyblue3", size=8) + 
  geom_edge_link(width=2) 

cowplot::plot_grid(p1, p2)

Themes

You can add on themes to your visualizations as well, theme_graph() (designed for networks) or theme_void() can work well

p1 + theme_minimal()

Labeling Nodes

We can use geom_node_text() or geom_node_label() to label our nodes.

ggraph(graph=net,) + 
  geom_edge_link() +  
  geom_node_label(aes(label=name)) 

Labeling Nodes

They also have a repel=T argument that will move the labels away from the center of the node.

ggraph(graph=net) + 
  geom_edge_link() +  geom_node_point() +
  geom_node_text(aes(label=name), repel=T) 

Labeling Your Plot

Finally you can label your plot with the labs() function

ggraph(graph=net) + 
  geom_edge_link() +  geom_node_point() +
  geom_node_text(aes(label=name), repel=T)  + labs(title="Sawmill Worker Network")

Layouts

Impact of layouts

Laying out a plot can impact how useful it is by a lot:

Layouts Two Broad Approaches:

• Dimension Reduction: Use multivariate techniques to scale into two dimensions
  • MDS, Pivot Scaling, Eigenvector
• Force-Directed: Simulates a physical process
  • Fruchterman and Reingold, Kamada and Kawai, Davidson-Harel, DrL, Large Graph Layout (LGL), Graphopt, GEM, and Stress majorisation

Force-Directed

In most of these layouts they do something like:

• Each node repulses all other nodes.
• Edges pull two nodes together.
• The balance of this is that groups of nodes with lots of connections are close and groups without them are far.

Fruchterman and Reingold Example

FR views vertexes as “atomic particles or celestial bodies, exerting attractive and repulsive forces from one another”.

How does this algorithm work?

1. Calculate the amount of repulsion between all nodes.
2. Calculate the amount of attraction between all adjacent nodes.
3. Move nodes based on the weight of attraction and repulsion, but limit the amount of movement by a temperature.
4. Reduce the temperature, go back to step 1.

Fruchterman and Reingold Example

Fruchterman and Reingold Example

Force-Directed Issues

• They are not guaranteed to get to the best layout. The initial starting values can matter a lot.
• They can take a lot of time to run if you have large networks.
• You can sometimes improve a layout by changing some of the parameters.

Force-Directed Examples

Setting Layouts

To set the layout you set layout= to what you want, you can also pass additional arguments as necessary.

If you want to create the exact same layout every time run set.seed() directly prior to making the plot. This sets the “random seed” that is used.

set.seed(1)
ggraph(graph=net, layout="fr", niter=250) + 
  geom_edge_link() +  geom_node_point(size=6)

Larger Networks

Issues

Working with larger networks can be difficult for a few reasons:

• The layouts can be computationally difficult.
• It quickly just becomes a ‘hairball’.

Solutions

There are a few useful things to do:

• Remove isolates or only visualize the largest component
• Remove edges with lower weights
• Think about what you are trying to visualize and emphasize that.
• Save the layout and reuse it.

Warning

If you are not showing the whole network you must make that clear.

Large Network - Ohio Donors

The Ohio data connects groups based on their shared donation patterns.

oh_edges <- read.csv("data/edge_OH.csv")
oh_nodes <- read.csv("data/meta_OH.csv")

oh_net <- graph_from_data_frame(oh_edges, vertices=oh_nodes, directed=F)
oh_layout <- create_layout(oh_net, "kk")
ggraph(oh_layout) + 
  geom_edge_link(color="gray") +  
  geom_node_point()

Large Network - Dropping Edges

We can drop the edges that aren’t “strong”:

oh_net <- delete_edges(oh_net,
    E(oh_net)[E(oh_net)$edge!="Strong"])
ggraph(graph=oh_net, "kk") + 
  geom_edge_link(color="gray") +  
  geom_node_point()

Large Network - Only Main Component

We can use the function largest_component() to grab just that part. Also the |> is a pipe which passes on the output.

oh_net |> largest_component() |> 
  ggraph("kk") + 
  geom_edge_link(color="gray") +  
  geom_node_point()

Why are we plotting this?

I don’t really care about the nodes themselves, what I care about is looking at how polarized this network is. There is a vertex attribute that shows the percentage of donations to Democratic candidates. Can we add that?

Adding Vertex Attribute

We can add vertex attributes to visuals on our network by using the aes() function inside of geom_node_point() and connecting the attribute name to the aesthetic we want to change:

geom_node_point(aes(color=degree))

Will color the node based on the vertex attribute named degree.

Changing the Scales

We can also change the scales using the scales_*_*() functions.

• scale_color_gradient(low="green", high="purple", midpoint=.5) - The color scale will go from green to purple with the midpoint at 0.5
• scale_size_continuous(trans="log10") - Will impose a log transformation.
• scale_fill_brewer(type="qual", palette=3) Fills things using a specific colorbrewer palette.
• scale_color_viridis_c() - Colorblind friendly colors.

Adding Vertex Attribute - Example

oh_net |> largest_component() |> 
  ggraph("kk") + 
  geom_edge_link(color="gray") +  
  geom_node_point(aes(color=PerDem)) + 
  scale_color_gradient2("% to Dems", low="red", high="blue", 
  midpoint=50)

Adding More Vertex Attribute

oh_net |> largest_component() |> 
  ggraph("kk") + 
  geom_edge_link(color="gray") +  
  geom_node_point(aes(color=PerDem, size=Total)) + 
  scale_color_gradient2("% to Dems", low="red", high="blue", 
  midpoint=50) + 
  scale_size_continuous("Total Donated", trans="log10")

Vertex Attributes

Vertex attributes are included for a variety of reasons. This includes:

• Demonstrating who is important in a network.
• Showing groups in a network.
• Presenting other relevant details

Directed Networks

New Network

This data is of Spanish high school students and includes negative and positive relations. We are going to delete the negative edges.

edges <- read.csv("data/spanish_hs_edges.csv")
nodes <- read.csv("data/spanish_hs_nodes.csv")
net <- graph_from_data_frame(edges, vertices=nodes, directed=T)
neg_edges <- which(E(net)$weight < 0)
net <- delete_edges(net, neg_edges)
net

IGRAPH 1bc71d6 DNW- 105 1058 -- 
+ attr: name (v/n), Colegio (v/n), Curso (v/n), Grupo (v/c), Sexo
| (v/c), prosocial (v/n), crttotal (v/n), X_pos (v/c), id (e/n), weight
| (e/n)
+ edges from 1bc71d6 (vertex names):
 [1] 3043->3047 3043->3087 3043->3093 3043->3065 3043->3097 3043->3044
 [7] 3043->3045 3043->3088 3043->3056 3043->3090 3043->3073 3043->3066
[13] 3043->3060 3043->3092 3043->3096 3043->3077 3043->3084 3043->3105
[19] 3043->3067 3043->3064 3043->3081 3043->3068 3043->3061 3043->3058
[25] 3043->3055 3043->3072 3043->3095 3043->3051 3043->3054 3043->3086
[31] 3043->3085 3043->3089 3043->3047 3043->3048 3043->3049 3043->3050
+ ... omitted several edges

Edges - Adding Arrows

Arrows are annoying to add here, but there is some good help online. We manualy create an arrow (arrow) and manually end them before the node (end_cap)

ggraph(graph=net, "stress") + 
  geom_edge_link(color="gray", 
    arrow = arrow(length = unit(4, 'mm')), 
    end_cap = circle(3, 'mm')) +    
  geom_node_point(aes(color=Sexo), size=4) 

Edges - Adding Arrows

Edges - Adding Attributes

Finally we can assign edge attributes to aesthetics

ggraph(graph=net, "stress") + 
  geom_edge_link(color="gray", aes(width=weight), 
    arrow = arrow(length = unit(4, 'mm')), 
    end_cap = circle(3, 'mm')) +    
  geom_node_point(aes(color=Sexo), size=4) 

Edges - Multiple

The default for ggraph is to show only a single edge when there are two mutual edges. We can change that by using geom_edge_fan()

ggraph(graph=net, "stress") + 
  geom_edge_fan(aes(color=weight),
    arrow = arrow(length = unit(4, 'mm')), 
    end_cap = circle(3, 'mm')) +    
  geom_node_point(aes(color=Sexo), size=4) 

Edges - Multiple

Modeling Networks

Difficulty

Modeling network is difficult as there are a lot of dependencies

• A calling B a friend might depend on if B calls A a friend.
• A calling B a friend might depend on if B calls C a friend.

Options

There are a few methods that have been developed:

• Exponential Random Graph Models (ERGMs)
• Stochastic Actor-Oriented Models (SAOMs)

Both attempt to model the complex interdependencies, I’m more familiar with ERGMs.

Where to go

• If you want to learn more about ERGMs: Inferential Network Analysis by Skyler J. Cranmer, Bruce A. Desmarais, and Jason W. Morgan
  • They will make heavy use of the statnet suite of packages.
• If you want more basic network knowledge (emphasis on graph theory): Networks by Mark Newman
• If you want a general intro to networks: Analyzing Social Networks in R by Stephen P. Borgatti, Martin G. Everett, Jeffrey C. Johnson, Filip Agneessens
  • Ignore their package

Other Things I Don’t Know About

• There are a variety of models to test how things flow in networks (and models to infer networks from flows).
• There are a few people who do experiments on networks (it is hard).