You have been building up skills and understanding about how ggraph works and now we’re ready to start building complex visualizations. Today we’ll work on different ways of showing power.
Power has long been a central concern of social scientists. The famous sociologist Max Weber defined it as the ability to control others or resources—to realize one’s will.
Some of this power comes in the form of “social capital”—the idea that there is power in our relationships—through mobilizing the resources of those we are connected to.
The construct of network power has many facets and over the years social network analysts have come up with a number of different algorithms for measuring different aspects of power in networks. These are usually called “centrality measures”. The intuition is that those in the center of a visualized network are typically those with the most power.
Degree centrality is simply the number of connections that someone has. For directed networks, indegree can be interpreted as popularity and outdegree as gregariousness.
Let’s look at different measures of power in the ht_friends network. There are a few new things going on here, so I’ll walk through each line:
ht_friends |> as_tbl_graph(): Hopefully you know what these lines do—take the ht_friends network and make it into a tidygraph object.activate(nodes) |> mutate(name = 1:nrow(.N())) adds a column called name to the nodes, which starts at the number one and goes to the number of nodes (nrow(.N())).geom_edge_fan(aes(alpha = stat(index))): This is where things get a bit tricky. This creates edges using the geom_edge_fan style and sets the transparency (alpha) of an edge so that it’s darkest closest to the to node. It’s for helping us see the direction of directed edges.geom_node_point(color = '#ceb888', size = 5): This should look familiar. It just sets a color and size for nodesgeom_node_text(aes(label = name)): This adds the labels we created earlier to the nodes. It just makes it easier for us to talk about individual nodes.guides(edge_alpha = guide_edge_direction(title="Direction", labels = c('from', 'to'))) This adds a legend to the plot that tells us what the alpha (transparency) of the edges means.G <- ht_friends |>
as_tbl_graph() |>
activate(nodes) |>
mutate(name=1:nrow(.N()))
G |>
ggraph() +
geom_edge_fan(aes(alpha = stat(index))) + # This does gradients for directed edges
geom_node_point(color = '#ceb888', size = 5) +
geom_node_text(aes(label = name)) + # Adds labels to nodes
guides(edge_alpha = guide_edge_direction(title="Direction", labels = c('from', 'to'))) # Adds the "Edge direction" legend
Now, let’s show the degree centrality by changing the size of nodes. Here is the total degree centrality. Note that we are using mutate to create the degree column, and then using it to adjust the size of the nodes.
G |>
activate(nodes) |>
mutate(degree = centrality_degree(mode = 'all')) |>
ggraph() +
geom_edge_fan(aes(alpha = stat(index))) + # This does gradients for directed edges
geom_node_point(aes(size = degree), color = '#ceb888') +
geom_node_text(aes(label = name, size=degree *1.1)) +
guides(edge_alpha = guide_edge_direction(title="Direction", labels = c('from', 'to'))) + # Adds the "Edge direction" legend
scale_size(name='Total Degree') # Can you figure out what this is doing?
Note how this changes when we show indegree/popularity
G |>
activate(nodes) |>
mutate(degree = centrality_degree(mode = 'in')) |>
ggraph() +
geom_edge_fan(aes(alpha = stat(index))) + # This does gradients for directed edges
geom_node_point(aes(size = degree), color = '#ceb888') +
geom_node_text(aes(label = name, size=degree * 1.1)) +
guides(edge_alpha = guide_edge_direction(title="Direction", labels = c('from', 'to'))) + # Adds the "Edge direction" legend
scale_size_continuous(name='Indegree')
This measure tries to capture how much a node is literally in the center of a graph. It is a measure of the average distance to each other node.
Note that there is a mode parameter that can be either ‘out’ for only outgoing distance, ‘in’, for incoming distance, or ‘all’, which we use, which ignores whether an edge is incoming or outgoing. If we don’t include the parameter, then it uses the default, which is ‘all’.
G |>
activate(nodes) |>
mutate(centrality = centrality_closeness(mode='all')) |>
mutate(centrality = replace_na(centrality, 0)) |>
ggraph() +
geom_edge_fan(aes(alpha = stat(index))) + # This does gradients for directed edges
geom_node_point(aes(size = centrality), color = '#ceb888') +
geom_node_text(aes(label=name, size=centrality)) +
guides(edge_alpha = guide_edge_direction(title="Direction", labels = c('from', 'to'))) + # Adds the "Edge direction" legend
scale_size_continuous(name = "Closeness Centrality")
This measure counts the number of shortest paths that go through each node. This is based on the value of being in a “structural hole”.
The last important measure of centrality is eigenvector centrality. The calculation is complicated and based on matrix algebra but the concept is pretty simple: all else being equal, a node is more powerful if it’s connected to a node that’s well-connected.
This is actually the basis of Google’s original search algorithm, and is part of what made it successful.
G |>
activate(nodes) |>
mutate(centrality = centrality_eigen(directed = TRUE)) |>
ggraph() +
geom_edge_fan(aes(alpha = stat(index))) + # This does gradients for directed edges
geom_node_point(aes(size = centrality), color = '#ceb888') +
geom_node_text(aes(label = name, size = centrality * 1.2)) +
guides(edge_alpha = guide_edge_direction(title="Direction", labels = c('from', 'to'))) + # Adds the "Edge direction" legend
scale_size_continuous(name = "Eigenvector Centrality")
What can we learn about this network by comparing indegree and outdegree centrality? What nodes appear differently in the two visualizations? What might that tell us about how these people operate in this group?
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What does this visualization tell you about the relationship between tenure and power in this network?
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