Twitter Follow Network for Political Networks Conference

I am currently attending the 5th Annual Political Networks Conference in beautiful Boulder, CO.  On twitter, the conference is served by the account @PolNetworks and the hash tag #PolNet2012.  Just for fun, below is a depiction of the follow network for the @PolNetworks account and all the twitter users who follow @PolNetworks.


Figure: Best described as the first-degree egocentric follow network of @PolNetworks.  Click the picture for a larger version.

This is a directed graph.  Arrows point from follower to followee.  Obviously, PolNetworks is in the center of this graph, because every user follows PolNetworks.

Graph Density:  0.15

Graph Transitivity:  0.56

Graph Connectedness:  1.00

Graph Efficiency:  0.87

Some Node-Level Measures:

Account inDegree outDegree Eigen. Centrality
JaciKettler 8 14 0.36
smotus 23 12 0.32
kwcollins 14 12 0.31
jlove1982 6 9 0.28
JohnCluverius 7 9 0.28
JeffGulati 6 9 0.25
RebeccaHannagan 2 8 0.24
therriaultphd 12 8 0.23
BrendanNyhan 21 9 0.21
davekarpf 7 7 0.21
richardmskinner 6 8 0.21
ianpcook 3 7 0.2
hsquared47 3 7 0.19
jon_m_rob 0 6 0.16
sissenberg 7 6 0.16
First_Street 1 6 0.15
FHQ 12 4 0.1
heathbrown 2 5 0.1
DocPolitics 1 4 0.09
ajungherr 0 3 0.07
archimedino 0 3 0.07
GeoffLorenz 0 3 0.07
JoeLenski 2 4 0.07
slimbock 0 2 0.05
James_H_Fowler 2 3 0.04
PolNetworks 34 1 0.04
jasonjones_jjj 1 3 0.03
krmckelv 1 2 0.03
dogaker 0 1 0.01
DominikBatorski 0 1 0.01
janschulz 0 1 0.01
jboxstef 0 1 0.01
matthewhitt 0 1 0.01
ophastings 0 1 0.01
stefanjwojcik 0 1 0.01

Edge list in xlsx format:  polnetworks_edge_list

Data collected 6/12/2012

Employment Progression

In my new dataset, each row is a series of jobs that one person has had.

Most of them are quotidian:
Junior Tax Analyst –> Senior Tax Analyst
Investment Banking –> Investment Banking –> Investment Banking

Some of them are funny:
Corn Detassler –> Flight Delivery Center Technician
Quabbity Assuance –> Electronics Sales Associate

Some baffling:
Gymnast –> Air Traffic Controller
bust boy –> bust boy –> bust boy?

And some inspiring:
Dishwasher –> Dishwasher –> Model

Does Barack Obama follow Queen Noor?

Twitter maintains a few lists of verified accounts. One of these lists includes 38 world leaders. Using Twitter’s fantastic API, I did some detective work to see which world leaders “follow” which others.

Follow network of verified world leaders’ Twitter accounts.

The graph is messy, but it displays some order. Barack Obama (@BarackObama) and David Cameron (@Number10gov) tie for the most followers at 17 each and appear toward the center of the network. The Prime Minister is more reciprocal in his attention – with 13 outgoing follows to The President’s mere 4.

What does it mean for one world leader to follow another on Twitter? Probably not much. Perhaps there will come a day when it is a diplomatic faux pas to meet with a head of state and then neglect to follow his Twitter account.

As for whether Barack Obama follows Queen Noor? He does not. @QueenNoor‘s follow of @BarackObama is unrequited.

Learning a Lattice is Easier than Learning an Irregular Graph (Sometimes)

If you made a picture of your social network, what would it look like? Would it look like a regular structure, like a lattice? Or would there be strange detours and crazy long-range connections between your friends’ friends?

Jason's Friendship Network

Jason's Friendship Network

It would probably be something more like the irregular graph than the lattice. People don’t form friendships in a regular, orderly manner conforming to strict rules of structure. Instead, people form local clusters of friends (you can call them cliques) and some people act as bridges between cliques to connect them and form the small-world topography familiar to social networks.

Ring Lattice Network

Ring Lattice Network

This is one of the points Watts and Strogatz illustrated with their social network models. A ring lattice may be a poor analog for a real-life friendship network, but a ring lattice with a few perturbations of the edges does a good job of capturing two characteristics of social graphs: local structure and random edges that allow a small world.

Watts & Strogatz Perturbations of a Ring Lattice

Watts & Strogatz Perturbations of a Ring Lattice

What would happen if we asked people to learn “who is friends with whom” in a ring-lattice social network or a perturbed Watts & Strogatz network? Will the regularity of the lattice structure make it easier to learn, or will it be difficult to learn because it goes against one’s expectations of how friendship clusters work?

The answer depends on the mode of presentation of the network. If the network is presented visually, as a network diagram, subjects learn the perfect Ring Lattice more easily than the perturbed version. However, if the network is presented simply as a list of connected nodes, the two graphs are equally easy (or hard) to acquire.

Accuracy by Training Type and Graph Type

Accuracy by Training Type and Graph Type

Diagram training allows for simple strategies. Names that are close together spatially in a Ring Lattice diagram are necessarily friends. This is true to some degree for the perturbed lattice as well, but it is not as reliable a strategy.

Diagram Training is Better than Edge Training

Remember when I told you that Learning a Social Graph Does NOT Depend on Method of Training? Well, I just hadn’t found the right type of training yet.

In fact, the results of one of my recent experiments suggest that using a diagram to teach subjects “what is connected to what” is better than telling them explicitly what is connected to what. Below are two images based on the stimuli the subjects saw.

Diagram Training Stimulus

Diagram Training Stimulus

Edge Training Stimulus

Edge Training Stimulus

The experimental manipulation was within-subject, so I could compare subjects’ own performance across the two types of training. Given the same amount of training, subjects answer more questions about the structure of the graph correctly in the Diagram Training condition than they do in the Node-Centric Edge Training condition.

Accuracy by Training Type and Graph Type

Accuracy by Training Type and Graph Type

You may notice that subjects learned two types of graph in addition to enduring two types of training. Stay tuned for a post about Ring Lattice graphs versus RingWatts graphs. I will also link to the manuscript with all the gory details of design and method when that manuscript is finished.

Learning a Social Graph Does NOT Depend on Method of Training

Learning a social graph does NOT depend on method of training. So far, at least.

One of my initial hypotheses when I began to study the acquisition of social network structure was this:

Some forms of representation of the network will lead to faster acquisition than others.

What I meant was that there are many ways you can represent a social network. You can put people’s names in circles and draw lines between the circles to represent relationships. You could simply list all the dyads – pairs of people who are friends, for example. Formally, you might create an adjacency matrix. Some of these should make learning who is connected to whom easy and some should make it less easy, right?

Well, not so far. However, I’m just beginning to explore the space, and the manipulations I’ve implemented so far may be too subtly different. For instance, I first trained subjects by either Random Edge or Network Walk training.

In Random Edge training, subjects were told they would be shown one dyad at a time – two names representing a pair of people who were friends. The friendships shown to the subjects were randomly drawn from the set of existing friendships. (An “edge” in a graph is a connection between two nodes.)

In Network Walk training, subjects similarly saw pairs of friends’ names. However, one name in each pair was always the same as a name in the previous pair. For example, a subject would see the sequence Frank-Bob, Bob-Alice, Alice-Cindy. Unlike Random Edge training, this type of training emphasizes the larger structure of the graph by taking you on a “walk” through the “network.”

This does not seem to make much difference to learners, however. In the graph below, you will notice that the type of training (Edge = Random Edge and Walk = Network Walk) makes no difference in how quickly subjects acquire information.

Random Edge vs. Network Walk Training

The type of graph affects speed of acquisition as expected. Random graphs take longer to learn than scale-free graphs.

The similarity in the pace of acquisition can also be conveyed in the form of learning curves. Here we see the number of errors decline as subjects are given more and more of each type of training.

Learning Curves - Random Edge vs. Network Walk

The difference between the two curves is not statistically reliable. Most of the confidence intervals around the data points overlap.

What should we make of the very similar performance for these two types of training? Being presented the connections in a graph in a systematic way (walking from edge to edge) seems to present no advantage over being given the list of edges in a random order. Of course, there is the usual caution about not accepting the null hypothesis. It may be the effect is just very small, and the experiment lacked power. However, the same experiment was powerful enough to detect the difference between random graph and scale-free graph acquistion rates, so if nothing else we can assume any possible effect is smaller than the graph structure effect.

I am still convinced there must be better and worse ways to learn the structure of a graph, and I’ll be experimenting with various training methods over the coming months. Check the blog for new results!