Q1. One premise of the Strength of Weak Tie theory is that, the stronger the tie between two people is, the more likely their contacts will overlap so that they will have common ties with the same third parties. Test this hypothesis for the les miserables graph we studied in class. The following code prints the number of shared neighbors for the endpoints of every edge:

for(i in E(g)){
a = ends(g, i)[1]
b = ends(g, i)[2]
source_neighbors = neighbors(g, a)
target_neighbors = neighbors(g, b)
num_overlap_neighbors = length(intersection(source_neighbors, target_neighbors))
print(num_overlap_neighbors)
}

Rewrite it as a function, use sapply() to apply the function to E(g) to get a vector as output. Then run a regression with the tie strength (measured as the edge weight, which is the value attribute) as the dependent variable and the number of shared neighbors as the independent variable. What do you conclude?

Q2.

For Hillary Clinton's email network we studied in class (with Hillary removed, i.e., the hillary_egocentric graph), create a new attribute "n_emails" for each node, defined as the number of emails received. Use 0 if no email was received.

a. Use the option vertex.size = log(V(hillary_egocentric)$n_emails + 1) to scale the size of the nodes, so larger nodes are the nodes that received more emails. Show your graph.

b. Run a regression using n_emails as the dependent variable and the normalized betweenness centrality of nodes as the independent variable. What is your conclusion?