Category Archives: social networks

Learning How Things Go Together

[This is my attempt at converting my dissertation abstract to “Up-Goer Five speak” (i.e. using only the 1000 most-frequently used English words).  For context, here’s the xkcd comic that started the trend.  Search the #upgoer5 hashtag on Twitter for more.  Try it yourself on the Up-Goer Five text editor.]

Big things are just many small things put together. It would be good to know which small things go together. You could learn how a brain works by thinking this way. Or you could learn which people like which other people. Thinking about how small things are put together to make big things is a good idea. It would be good to know how we learn, and how we should learn which things go together.

To this end, I did five studies in which people learned which things in a set were joined together. To show you what I mean, some people learned “who is friends with who” in a friend group. But other people learned about other things that were joined together – like which cities have roads that go between them. By doing these studies, I found out a few things. One thing I learned was that it matters how the things are joined up. To show you what I mean, think about the friend group again. It is easier to learn who is friends with who in a group where few people have many friends and many people have few friends. If things are more even, and all people have about the same number of friends, it is hard to learn exactly who is friends with who.

It doesn’t matter if the joined things are people or cities or computers. It is all the same. Also, it doesn’t seem to matter much why it is you are learning what things go together.

I also show that people learn better by seeing a picture of joined-together things rather than reading about joined-together things. This is the case even more when the things that are joined are made to be close together in the picture.

Finally, I talk about an all-around idea for how people learn about groups of joined together things. I say people start out by quickly sorting things into much-joined and few-joined types. Then they more slowly learn which one thing is joined to which one other thing a little at a time.


London 2012 Twitter Olympics

The London 2012 Olympics are upon us.  Lots of athletes will be judged, timed and measured for the athletic things they do.  But aren’t the non-athletic things they do much more interesting?  Like tweeting?

No, of course not.  But that’s not going to stop me from holding my very own Twitter Olympics and handing out (virtual) medals for exceptional Twitter performances.

Below is the list of events and the results so far.  I’ll be rolling out more results as the real Olympics go on.

Preview Event: Games-Dropping

  • Who’s most pumped up for the games? In this event, Olympians score one point for every time they have used the words Olympics, Games, or London in their recent tweets.
Olympian Games, Olympics or London in Tweets
@SwissDom 41
@lolojones 37
@NickSymmonds 28

Full Results:  london2012_gamesd (.xlsx)

Sexy At-Mention

  • In this event, a sampling of thousands of tweets mentioning Olympic athletes was scored. The winning Olympian was the one with the most co-occurrences of their Twitter handle and the words “sexy,” “hottest,” “beautiful,” “cute,” “handsome,” “pretty,” or “babe.”
Olympian Sexy At-Mentions
@matthew_mitcham 25
@Joeingles7 8
@hopesolo 7

Full Results:  london2012_sexy (.xlsx)

The Sesquipedaliathon

  • In this event, scores are awarded based on the average number of syllables per word in the Olympian’s tweets.
Olympian Syllabes Per Word Longest Word
@juanmata10 1.76 visitaremos
@Njr92 1.66 spideranderson
@TipsarevicJanko 1.62 pantomime

Full Results:  london2012_sesq

Most Followed

  • In this event, one point is scored for each Twitter follower.
Olympian Followers
@Njr92 4,953,514
@juanmata10 1,164,329
@DjokerNole 1,111,326

Full Results:  london2012_user_info

Most Followed (by other Olympians)

  • In this event, one point is scored for each Olympian follower.
Olympian Fellow Olympian Followers
@MichaelPhelps 12
@usainbolt 11
@lolojones 9

Full Results:  london2012_degrees

London 2012 Olympians Twitter Follow Network

London 2012 Olympians Twitter Follow Network.  Arrows point from follower to followee.  Click the picture to view a larger version.

Most Follows

  • In this event, one point is scored for each Twitter user the Olympian follows.
Olympian Followees
@officialasafa 3,794
@Njr92 630
@TomDaley1994 542

Full Results: london2012_user_info

Most Follows (of other Olympians)

  • In this event, one point is scored for each fellow Olympian the Olympian follows.
Olympian Follows X Fellow Olympians
@ItsStephRice 8
@OscarPistorius 7
@RickyBerens 7
@drewsullivan8 6
@matthew_mitcham 6
@MichaelPhelps 6
@PopsMBonsu 6

Full Results: london2012_degrees

Special Event: Non-Olympian Most Followed by Olympians

  • The only event (so far) in which non-Olympians compete. Medals to those non-Olympians who are followed by the most Olympians.
Non-Olympian Name Olympian Followers
@OMGFacts OMG Facts 10
@SportsCenter SportsCenter 9
@espn ESPN 8
@Sports_Greats Sports Quotes 8

Full Results:  london2012_nonlist_followees

Olympic Followback

  • Most athletes have many more followERS than followEES. In this event, Olympians are scored according the proportion of their followers that they follow back.
Olympian Followback Percentage
@drewsullivan8 16.7%
@SmoothKJ88 14.2%
@EricBoateng 10.1%

Full Results:  london2012_followback


Olympians on Twitter Olympics

The Olympics bring together the world’s most talented and dedicated athletes.  And so does Twitter.  As a part of my continuing effort to try to do interesting things with the Twitter API, I decided to create my own Olympics for Olympians on Twitter. Er, yeah I think that’s right.

To begin with I created the sociomatrix of Olympian Tweeters.  A sociomatrix is a table where every person in a group gets a row and a column.  Each cell in the table indicates whether a relationship exists between two people (the row person and the column person).  To indicate this, one just places a zero in the cell if the relationship does not exist and one if it does.

Jack Rose Cal
Jack 1 0
Rose 1 0
Cal 0 1

Example Sociomatrix.  The relationship is row in love with column as per James Cameron’s Titanic.

I created a sociomatrix of Olympians on Twitter where the relationship was follows.  Given a sociomatrix, row sums and columns sums are usually interesting, quick summaries of the data.  In our case, a row sum is the number of Olympians one particular account follows.  A column sum is the number of Olympians following a given account.  So, without further ado, let’s get to our first event:  Olympian most followed by other Olympians.

Most Followed (by other Olympians)

Medal Olympian Followed By
Gold @BillyDemong 30
Gold @Shaun_White 30
Gold @ApoloOhno 30
Silver @lindseyvonn 28
Silver @emilycook 28
Bronze @GretchenBleiler 25

Do they allow ties in the real Olympics?  Probably not, but since these are virtual gold medals I’m handing out, why not?

You can probably guess the next event.  And this would probably be the easiest event to win if you knew it was coming.  We know who has the most followers, but who does the most following?

Most Follows (of Olympians)

Medal Olympian Follows
Gold @emilycook 73
Silver @StevenHolcomb 34
Bronze @TFletchernordic 32

The Sesquipedaliathon

Medal Olympian Syllables per word Longest word
Gold @LMCHOLEWINSKI 1.88   obesity
Silver @AngelaRuggiero 1.58   sustainability
Bronze @Pchiddy 1.57   anniversary

In the sesquipedaliathon, Olympians compete on their vocabularies.  Tweeters are ranked by the mean number of syllables in the words in their tweets.  Polysyllabic expressions win out over short words.

Sesquipedalian tweets may be the mark of a skilled wordsmith discussing a complex topic, or they may be the result of needless pretentiousness.  Syllables per word is one component of the Flesch-Kincaid readability scale.  According to the Flesch-Kincaid scale, the more syllables-per-word one uses, the more sophisticated the writing (or the less readable the text, depending on how you want to look at it).

The gold winner @LMCHOLEWINSKI is tweeting at about a 10th grade level.  @LMCHOLEWINSKI’s tweets clock in at about the same level as the discourse in the United States Congress,  according to recent analyses.

(For fun, I checked the syllables per word my dissertation tweetbot outputs.  At 1.61, my doctoral dissertation would take home a silver.)


Medal Olympian Tweets about “Games” or “Olympics”
Gold @ShaniDavis 19
Silver @AngelaRuggiero 17
Bronze @GretchenBleiler 16

For this event, Olympians score every time they use the word “games” or “Olympics.”  So the medal winners are (presumably) those who are talking about the Olympics most often.

Sexy At-Mentions

Medal Olympian Sexy At-Mentions
Gold @vitya_zvesda 16
Silver @lindseyvonn 15
Bronze @louievito 11

Yes, it has come to this.  I needed to find something to do with at-mentions, right?  So why not count for each Olympian how many times someone calls them sexy in a tweet?  And why stop with sexy?

One point for each tweet that mentions the athlete by their twitter handle and also contains one of the following words: hot, sexy, babe, handsome, pretty, beautiful or cute.

Non-Olympian Most Followed by Olympians


Medal Tweeter Olympians Following
Gold @lancearmstrong 30
Silver @ConanOBrien 24
Bronze @BarackObama 20
Bronze @TheEllenShow 20
Bronze @StephenAtHome 20
Bronze @universalsports 20
Bronze @shitmydadsays 20

This event was the toughest – as far as programming time goes.  First, I grabbed everyone my list of Olympians follow.  Then I aggregated to find out exactly how many Olympians followed each account.  Then I filtered out Olympians to get this list of non-Olympians most followed by Olympians.

That’s the last of the events for now.  Please check below for updates, and leave ideas for new Twitter Olympics events in the comments!


UPDATE: The list of Olympians used here came straight from Twitter’s verified accounts page.  However, it’s rather wonky.  I have a new, better list of London 2012 Olympians on Twitter and I’ll be re-running all of these analyses on this list.  Check for a link to the London 2012 version of these events on Friday the 27th.

UPDATE: London 2012 Twitter Olympics now available.

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

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.