Weak Ties and Small Worlds

Dad Joke

My wife asked me to put ketchup on the shopping list.

Now I can’t read it at all!

Housekeeping

  • Sorry for the schedule confusion!
  • Final project idea due next week
  • Social Search assignment due March 23
    • Try to find someone with driver’s license from HI
    • No group texts
    • Diagram search network
    • Instructions on website

Also upcoming

  • Visualization Challenge
    • Start from existing dataset (Dutch school student behavior or Harry Potter)
    • Come up with a question
    • Create a network visualization that helps to answer that question
    • Working in pairs is great

Anatomy of ggraph

G |> 
activate(nodes) |> 
mutate(centrality = centrality_eigen()) |> 
ggraph(layout = 'kk') + 
geom_edge_fan(aes(width=weight), color = 'gray') + 
geom_node_point(aes(size=centrality), color = 'gold')

Loads the graph, which is stored as the variable G (the |> sends the output to the next line)

Selects the nodes “spreadsheet” to edit. To activate the edges, run activate(edges)

Calculates the eigenvector centrality and saves it as a new column in the nodes spreadsheet. Note that we keep using |> until we get to ggraph()

Tells R we want to take the network and make a plot from it. This is where we set the layout

Remember to add edges first.

The first argument is the “aesthetic mapping” - this maps aspects of the plot to variables in your data. In this case, we change the width of the edges based on the variable “weight”, which must be in our edges “spreadsheet”

We can also change the look of the plot universally. These options go outside of aes()

This code does similar operations to the nodes. It changes the size based on the centrality (which we calculated and defined in line 3) and changes the color of all nodes to gold

Review Questions

  • What is a “path”? What is the “path length” of a path?
  • What is the “geodesic distance” or “diameter” of a network?
  • What is triadic closure?
  • Why would we expect networks with high triadic closure to have high geodesic distance?

Review Questions

  • What was the Travers and Milgram experiment?
  • How can we have such high triadic closure but still have short path lengths? What was the key insight from Watts and Strogatz?
  • What does this have to do with Granovetter (weak ties)?
  • What is similar to “random rewiring” in real life?

Break!

Discussion Questions

  • What are some of your best “small world” moments and what were the connections?
  • Is the small world smaller now?
  • To what extent do psychological factors (motivation, uncertainty, etc.), shape social chains?
  • How does homophily affect the small world phenomenon?

Discussion Questions

  • If the network shapes who you meet, who you marry, what jobs you get, what ideas you’re exposed to, how much of who you are was actually chosen vs. just a product of your position in a network?
  • Travers and Milgram found evidence of “funneling” through certain individuals, while Dodds suggests hubs are less important. Is this difference due to scale (U.S. based vs global), technology, (mail vs. email), or changes in network structures over time?

R Co-working time