(1) the data sandwich, AGAIN

library(dataculture)
library(igraph)
library(ggraph)

The ggraph package incorporates, as example data, a variable whigs. Enter whigs on its own, and help(whigs) to see the documentation. As it happens, the Rutgers library has digital access to David Hackett Fischer’s Paul Revere’s Ride (Oxford: Oxford University Press, 1995).

1. Look at Hackett’s Appendix D (301–7) at https://hdl-handle-net.proxy.libraries.rutgers.edu/2027/heb31559.0001.001.

   1. How were these pages used to create whigs, and by whom?
   2. How did Hackett create these pages? (Hint: scholarship has citations.)

2. Han discusses five groups in his analysis of Fischer’s data.

   1. How many groups are represented in whigs?
   2. What’s the reason for the difference? (Hint: “Data Sources and Methods.”)

To follow Han, you have to drop some columns, then drop the rows corresponding to people who belong to none of the remaining groups. The following incantation¹ does this:

# remove columns 5 and 7
whig_han <- whigs[ , -c(5, 7)]
# keep rows whose sum is strictly positive
whig_han <- whig_han[rowSums(whig_han) > 0, ]

The following line creates a variable with the bipartite graph of Boston revolutionaries and their groups. igraph calls an affiliation matrix an “incidence matrix.”

whig_net <- graph_from_incidence_matrix(whig_han)

Ties by eye

1. Make the hairball using ggraph. Use a color aesthetic with geom_node_point to distinguish persons and groups. Work with your group members to recall the syntax from the previous lab.

   1. Look carefully at the plot. Where are the three people who seem to play an especially important role tying others together?

   2. Identify the people by putting in the node labels (recall the previous lab).

2. Han of course has already told you who these people are. In the previous lab, you learned how to cut vertices out of graph. To cut more than one, you can use something like c("Hamlet", "Claudius") where you would put just "Hamlet".

   1. Cut them out of the network, make plots again, and describe what happens.

The strength of weak ties

Now try the following:

P <- whig_han %*% t(whig_han)
G <- t(whig_han) %*% whig_han
wp <- graph_from_adjacency_matrix(P, weighted="strength",
                                  mode="undirected")
wg <- graph_from_adjacency_matrix(G, weighted="strength",
                                  mode="undirected")

1. What are these four variables? Without needing to know what %*% and t do, a little printing out and perhaps plotting ought to be enough to let you guess.

   1. weighted="strength" creates a new edge attribute, strength. Both wp and wg have extra information attached to each edge, a strength number. What is this? If you look at G you should be able to figure it out.

2. Plot wg. Try geom_edge_fan(aes(alpha=strength)).

3. Plot wp, again visualizing the edge strength.

   1. Explain in network terms what seems notable about the three “central” figures.

Han uses some quantitative measures of bridging to support his argument. Measures of bridging usually depend on the idea of a “geodesic” or shortest path between nodes.

The betweenness of an edge is the proportion of all geodesics between pairs of nodes that include that edge. This can be calculated with a special igraph function, edge_betweenness. The following code creates a data frame with rows for each edge of wp and columns for edge betweenness and strength:

wp_edge_stats <- tibble(
    eb=edge_betweenness(wp),
    strength=edge_attr(wp, "strength"))

4. Make a scatterplot (not a network diagram) of edge betweenness against strength (use jitter since there are only a smaller number of possible values). What does this reveal about weak ties and connectivity?

A similar measure exists for nodes. The betweenness centrality of a node is the fraction of all geodesics between pairs of nodes that pass through that node.

The special function centrality_betweenness() (nothing inside the parentheses) can be used inside an aes specification for a geom_node_*. (It sometimes generates silly warnings about nobigint which you can ignore.)²

5. Make a plot of the network of persons wp in which the size of a node is proportional to its betweenness centrality. Who stands out?

The transitivity function calculates the clustering coefficient, but getting this data into a comparable visualization is slightly annoying. Here is some code to help you get there by adding a transitivity attribute to the nodes of wp.

V(wp)$transitivity <- transitivity(wp, type="local")

6. Now make a network plot of wp in which the size is proportional to transitivity, and compare to the previous plot.