EVERYBODY LINKS TO SPIDER-MAN
Degree distributions on linear and log-log axes, in-degree against out-degree, the giant component drawn out, and the one island that refuses to touch the rest of the universe.
Course project for 02805 Social Graphs and Interactions, Technical University of Denmark.
Every week of the course brings a new topic, and every week we do the same things with it. We ask a question that numbers can answer and write the answer up as a post, with the figures, the dead ends and the checks. And we build something you can play with: a game that turns the week's idea into something you do instead of read, or an explorable that lets you turn the knobs yourself.
Degree distributions on linear and log-log axes, in-degree against out-degree, the giant component drawn out, and the one island that refuses to touch the rest of the universe.
A proper power-law fit and what it cannot say, the friendship paradox and the two characters nobody out-popularities, twelve numbers shuffle-tested against two nulls, a preferential-attachment Marvel next to the real one, and the villains crawled in.
Four definitions of importance and the shuffle test that sorts them: Spider-Man's famous betweenness is just his degree, the real brokers are Black Widow, Hercules and a forgotten character with two links, and the biggest clique is six X-Men with two guest chairs.
A change of guests: every philosopher on Wikipedia born before 1900. Communities as tables at a dinner, modularity as the score, Louvain against a shuffled network, a greedy merger and a historian, and the finding that Louvain cannot decide where Aristotle sits.
The network gets its text. Every link becomes the sentence that carries it, parsed and labelled foe, ally or family: foes cross communities like any link, family never does. Zipf on 718,552 tokens, Wikipedia copying itself, a search engine that cannot find Thor because he is not there.
TF-IDF put Storm next to the Human Torch because of a surname. We split every cosine similarity exactly into names, habit words and everything else: 99 percent of the strongest lookalikes are names, half of the text's agreement with the network is names, and the story twins are linked no more than two random pages.
A slot is reserved. It fills in when week 7 lands, with its post and something to play.
A slot is reserved. It fills in when week 8 lands, with its post and something to play.
Eight things to play with, newest first: five games and three explorables. A game scores you against something; an explorable lets you turn the knobs. Each one is built on the week's idea and the data we were working with that week.
Describe a secret Marvel character one word at a time while a cosine-similarity machine ranks all 303 Wikipedia pages against your words. You win when yours is first; names are taboo and cost a strike. Allow names and one word wins almost every time, which is the whole week in one switch.
Play itPick a Marvel page and watch its textual lookalikes re-rank while you turn two dials: how much names count and how much Wikipedia's habit words (she, her, voiced) count. Every neighbour is a bar split into names, habit words and everything else, and the network's agreement with the text is measured live as you drag.
Turn itEvery Marvel page reduced to a bag of words. Unmask the character from as few words as you can while a bag-of-words machine reads the same clues and commits on its own schedule; tell a real Wikipedia sentence from one a trigram model dreamed up; put the blanked word back into a concordance line. One case of the day for everyone, with a result to copy.
Play itYou get one philosopher at the head of an empty table and 3, 5 or 9 seats to fill. The score is the links inside the table beyond what chance would give, one table's share of modularity, and hubs are expensive. Then a greedy host, a random host and the best table we ever found sit down beside yours. Or host the whole room, 1374 philosophers and a handful of place cards, and take on Louvain.
Host itYou get eight hits. Remove characters from the real network and try to shatter its core; whoever loses their last route to the big cluster is cut off. Then three rival hitmen run the same contract: one shoots the most connected, one the biggest broker, one at random. The map shows who is popular. It does not show who holds the network together.
Play itWatch the Marvel universe grow one character at a time from 1939 to 2020, each arrival with its comic panel, with or without the villains, and see who collects the links. Then grow a preferential-attachment universe of the same size next to it. In the model, whoever arrives first becomes a hub. On Wikipedia, the hubs are the class of 1962.
Watch itGrow a network where newcomers attach with probability proportional to k to the power α, and turn α. Below 1 the hubs never form. At 1 you get Barabási-Albert. Above 1 one node takes a fixed share of every link, however big the network gets. Spider-Man reads 1.1 on the dial.
Turn itPick Spider-Man, Wolverine or Doctor Strange. You get sent somewhere out in the network and have to click your way home along real Wikipedia links, one page at a time. The map only exists where you have walked, and your score is measured against the shortest route that actually exists in the graph.
Play it