The Marvel network gets language

What a word is. A tokenizer decides where one word ends and the next begins. Unless a section says otherwise, a word is a run of letters, lowercased, with an apostrophe or hyphen inside it kept and a possessive 's removed: "Spider-Man's first appearance in 1962" gives spider-man, first, appearance, in. The pages then hold 713,617 tokens, word occurrences, of 27,754 types, different words.

A link from A to B means A's Wikipedia page links to B's. For each of the 1,784 links we took the first sentence on A's page that names B, and found one for 1,513 (85%). Most of the rest come from infoboxes and navigation boxes, which our copy of the text has lost; 33 point at one of 7 alternate versions, such as the film Jean Grey, whose name belongs to the main character.

A small word list labels each sentence: killed, family, enemy, ally or teammate. It matches lower-case words only, so a name such as Doctor Nemesis supplies no label. 836 of the sentences (55%) match no word at all.

The communities come from 100 LouvainA method that finds communities by moving nodes between groups until links inside the groups are as dense as it can make them. It starts at random, so two runs can differ. runs on the link network. For each label we counted how often its links join two different communities, averaged over the runs, and compared it with 1,000 shuffles of the labels over the 677 labelled links.

Each page splits into paragraphs at its line breaks and into sentences with spaCy's rule-based sentencizer. Sentences under References, External links, Notes, See also and Further reading are dropped. A character is found by its page title without the disambiguation ("Storm (Marvel Comics)" is "Storm") and by the real name its description gives in brackets ("Emil Blonsky" for the Abomination), as a whole word. A name several pages go by belongs to the main page: "Spider-Man" is the main Spider-Man, not the Mangaverse one.

A sentence that matches several labels takes the first of killed, family, enemy, ally, teammate. Negation is not handled. Louvain runs on the weighted, undirected link network with seeds 2805 to 2904. The runs disagree with each other, so the test uses how often each link crosses over all 100 runs, for the real labels and the shuffled ones alike.

The word list reads the sentence, not the pair: a long sentence that names B often tells of a third character. "Phyla then goes with Nova and Star-Lord to lead a final battle against Annihilus" makes Star-Lord her enemy.

A stricter shuffle only swaps labels between links that leave the same page, so a page written in hostile words throughout cannot carry the result. Enemies still cross more than it predicts (46%, \htmlClass{x-z}{z} = 3.6) and family less (33%, \htmlClass{x-z}{z} = −3.7). A pair of characters who link both ways counts twice above; counting each pair once gives \htmlClass{x-z}{z} = 3.6 for enemies and −4.0 for family.

The labelled links: 217 teammate, 202 enemy, 116 family, 84 killed and 58 ally. 113 sentences match more than one label.

We read 60 sentences, 12 per label, drawn at random: 32 of the labels describe how A and B relate. Ally labels hold up best (9 of 12), enemy and killed worst (5 of 12 each), family in between (6 of 12).

✓ means the label describes how A and B relate; ✗ says what the sentence is about instead.

We split every page into lower-case words, 740,282 in all, and collected every run of eight words in a row, an 8-gram. A run found on many pages is house style, not copying: "in American comic books published by Marvel Comics" is on 282 of the 303 pages. So 8-grams on more than 10 pages are set aside.

The remaining 8-grams merge into passages, overlapping runs counting once. Two pages copy each other when they share a passage of 30 words or more. The copying network links those pages, and its connected pieces are the clusters.

A word is a run of letters and digits, with an apostrophe inside a word kept ("jean's"); punctuation and line breaks are dropped. Each word keeps its place on the page, so every shared passage is quoted from the page itself, and a passage copied twice on a page counts twice. A passage is labelled with the section heading above it on each of the two pages. What ties each cluster's characters was read from their pages.

The check: a pair that copies is compared with all 45,753 pairs of pages and with the 2,830 pairs that share only a phrase, an 8-gram run shorter than 30 words. A link counts in either direction.

The text has no edit history, so we cannot tell who copied whom. The passage length matters: at 20 words, 80 pairs copy and 46 of them link; at 50 words, 11 copy and all of them link.

The two pairs that do not link are Wild Child's: his page shares a stock sentence about Krakoa with Storm's and Rachel Summers's. Five clusters share a codename (Venom and Eddie Brock), six a team (Rocket Raccoon and Star-Lord) and one a family.

The house-style cutoff barely matters: any cutoff from 3 to 20 pages gives the same 22 pairs. And runs of 12 words add 16 pairs from a templated lead that 8-word runs split, on eight Strikeforce: Morituri pages whose leads come in two versions.

The longest passage of the largest copying pair, quoted from its first page. The next two pairs, and a templated lead that only runs of 12 words find, are one click away.

A word is a run of letters and digits in any alphabet, lowercased, and a hyphen splits words, so Spider-Man counts as spider and man. The 303 pages and their 28,062 different words form a document-term matrix that is 97.2% empty. The most common word, the, makes up 6.1% of all 740,340 words: a handful of words dominate every page, as Zipf's law says.

The brief's own example, "Norse god of thunder", has no target: the snapshot holds no page for Thor, so it stays out of the hit rates.

Pages with equal cosine rank in node order, in the script and in the search box. A random ranking puts the target first with probability 1 in 303 and in the top five with 5 in 303; a binomial test gives each hit count its p-value.

With raw counts, 8 of the 10 misses are won by a page shorter than the median page of 1,258 words.

A miss is labelled from the data, for each model: a short-page win when the winning page has at most a third of the target's words, a missing word when the target shares no content word with the query, and otherwise a win by a page that is not short. The search box runs the stopword-free model on the same vocabulary as the table.

We chose the 12 queries and their targets ourselves, so the hit rate says how the search does on our questions, and the single first-place hit, Moon Knight, carries the raw headline.

Redneck's page wins "weather-controlling mutant from Kenya" while sharing one word with the query besides stopwords, mutant, in its first sentence:

First the communities. Louvain ran 100 times on the giant component of the link network, the 277 of 303 pages joined to each other by links. The runs disagree: they found 89 different partitions, the most common one in only 4 runs, and 77 runs found 8 groups. Two runs agree with a median normalised mutual informationNormalised mutual information: how much two splits into groups agree, from 0 (unrelated) to 1 (identical). of 0.90. So we kept a consensus: two pages share a group when at least half the runs put them together, which gives 8 groups, the same for all 100 seeds we tried on it. The 9 Strikeforce: Morituri pages link only to each other and form a ninth group; the 17 pages with no links have none.

A trigram model is next-token prediction, what a large language model does, with a two-word window and a table of counts in place of a neural network. Each fake page opens with one sentence we wrote by hand ("Aetherion is a character appearing in American comic books published by Marvel Comics.") and continues with 5 sentences the model samples word by word.

Before training we replace every character's name, the page title and the real name its description gives, by [name], so a guess cannot rest on spotting a member. The quiz shows these masked fakes.

Tokeniser: each page splits into paragraphs at its line breaks and into sentences with spaCy's rule-based sentencizer, which knows that "Dr." does not end a sentence. Heading lines are dropped, and so is every sentence under References, External links, Notes, See also and Further reading. A word is a run of letters in any alphabet, with an apostrophe or hyphen inside it kept, lowercased and with a possessive 's removed; digits and punctuation are dropped.

Each sentence is padded with two start markers and one end marker before counting. The model has no smoothing and no backoff: sampling starts from the start markers and only ever reaches two-word contexts that occur in the pages. A sentence that reaches 40 words without ending is thrown away and drawn again, never cut; that happened to 5 sentences. Names are matched as whole words with their capitals, so "Storm" becomes [name] and "storm" stays.

The mask covers only the 303 characters' own names. Other characters, surnames on their own and team names stay, and all 9 masked fakes keep some, such as mephisto, khonshu and krakoa, so a guess can still rest on a name.

The groups, named after their page with the most link weight: Hulk, 40 pages; Wolverine, 40; Spider-Man, 38; Scarlet Witch, 38; Quasar, 35; Doctor Strange, 34; Iron Fist, 30; Black Widow (Natasha Romanova), 22; Radian (Morituri), 9.

The groups shift from run to run, as the median normalised mutual information of 0.90 shows; the consensus keeps the pairs most runs agree on.

Without the mask, 7 of the 9 fakes name a member of their own group.

The links hold these groups together far more tightly than chance. Louvain's modularityA score for a split into groups: how many more links fall inside the groups than a random network with the same link counts would put there. averages 0.503 over the 100 runs, against 0.347 ± 0.004 on 100 rewired copies of the network (\htmlClass{x-z}{z} = 36.6). The consensus groups score 0.506. The rewiring swaps the ends of two links of equal weight, 50 swaps per link, so every page keeps its number of partners and its total link weight.

For every fake we searched its group's sentences for the longest run of words it repeats verbatim. The runs are 8 to 17 words long, and 8 of the 9 come from a single page. Opening the example gives away one quiz answer.

A token is one word as it occurs, a type one distinct word: "the Hulk smashes the tank" has 5 tokens and 4 types, since "the" comes twice. We read the 303 pages one after another, 713,617 tokens in all, and counted after every token how many types had appeared so far. The whole corpus holds 27,754 types.

Heaps' lawThe rule that the number of distinct words in a text grows as a power of its length below 1, so each new stretch of text brings fewer new words than the last. says that count grows as a power of the tokens read, \htmlClass{x-types-seen}{V} = \htmlClass{x-heaps-k}{K}\,\htmlClass{x-tokens-read}{n}^{\htmlClass{x-beta-heaps}{\beta}}, with \htmlClass{x-beta-heaps}{\beta} below 1: the more you have read, the more often a word is one you have met before. On Marvel \htmlClass{x-beta-heaps}{\beta} = 0.56, so reading 4 times as many words turns up about 2.2 times as many types.

A word is a run of letters in any alphabet with an inner apostrophe or hyphen kept, lowercased, with a possessive 's removed; digits and punctuation are dropped. So "Spider-Man's" and "Spider-Man" are one type and "Pérez" stays whole. Ties in link count are broken by the page's id. Every curve is read off on 41 token counts spaced evenly on a log scale from 1,000 tokens to the whole corpus.

The gap of an ordered curve to random is given in types and in z, the number of standard deviationsHow far values typically sit from their average. of the 500 random orders. Every order ends on the same 27,754 types, so the random spread shrinks to nothing near the end; the two token counts we quote stay well short of it.

The fit is a straight line through \htmlClass{x-log-fit}{\log} \htmlClass{x-types-seen}{V} against \htmlClass{x-log-fit}{\log} \htmlClass{x-tokens-read}{n} on the random orders' mean, over the 26 grid points from 11,750 to 713,617 tokens: \htmlClass{x-heaps-k}{K} = 16.7, \htmlClass{x-beta-heaps}{\beta} = 0.56. Fitted to each random order alone, \htmlClass{x-beta-heaps}{\beta} runs from 0.54 to 0.57 (5th to 95th percentile).

Pages differ in length, and the most-linked pages are the long ones. Shuffling in-degree only among pages of similar length, in fifths by word count, 500 times, leaves both gaps standing (\htmlClass{x-z}{z} = 3.2 for least-linked first at 100,000 tokens, \htmlClass{x-z}{z} = −2.8 for most-linked first at 400,000), but fifths hold length only roughly.

The gaps hold across the grid, not only at 100,000 and 400,000 tokens. The least-linked order stays 1.6 to 2.9 standard deviations above random from 11,750 to 266,346 tokens, and the most-linked order 2.0 to 3.9 below from 313,893 to 605,520 tokens. Each order leads or lags only while it reads its own end of the list: by 400,000 tokens the least-linked order has begun 253 pages, reached pages linked from 10 others, and sits at random (\htmlClass{x-z}{z} = 0.2).

Every count rests on one word rule; keeping digits or splitting hyphens would move them. And the link count only covers links among these 303 pages, not a character's fame in the comics: 58 of the pages get no link at all.

It bends but never flattens out. The slope on log-log axesA chart where both axes are logarithmic: each step along an axis multiplies the value by the same factor, so small and huge counts fit on one chart. is 0.63 below 91,570 tokens and 0.49 above, so new words come more slowly as the corpus grows. In the last tenth of the corpus the random orders still meet 18 new types per 1,000 tokens.

The last 100 pages in most-linked order, each linked from 2 pages or fewer, hold 90,907 tokens and add 2,144 types no earlier page used. 1,055 of them (49%) look like names, words that only ever occur with a capital letter, against 41% ± 1.6% for the last 100 pages of the random orders.

The split is a rough proxy: 53 of those names are capitalised only where they open a sentence or a line.

A character's in-degree is the number of the other pages that link to its page. We counted the words on each of the 303 pages by the rule sections 5 to 7 share: runs of letters in any alphabet, an inner apostrophe or hyphen kept, lowercased, a possessive 's removed; digits and punctuation dropped.

We fitted a straight line to \htmlClass{x-ln-length}{\ln}(\htmlClass{x-words-doc}{\text{words}}) against \htmlClass{x-ln-length}{\ln}(\htmlClass{x-log-shift}{1 +} \htmlClass{x-in-links}{\text{in-degree}}) by ordinary least squaresFitting a line by making the sum of the squared vertical distances from the points to the line as small as possible. over all 303 pages. The 1 + keeps the 58 pages nobody links to, 17 of them isolatesNodes with no links at all. with no links at all. The slope is 0.72: each doubling of 1 + in-degree multiplies the predicted length by 1.65, starting from 546 words at zero in-degree. A page's residualWhat is left of an observation once the model's prediction is taken out. is its distance from the line in natural-log units, so \htmlClass{x-exp}{\exp}(\htmlClass{x-residual-log}{\text{residual}}) is its length over the predicted length: ×2 means twice as long as the line predicts.

What we measured for each of the ten: whether the page is an isolate; how many other pages name the character and how many of those link to it, where a name is its title without the disambiguation plus the real name its node description gives in brackets, as in section 1; whether the page is for a codename several characters share, which we call a hub page (its first sentence says several characters share its title, the rule section 7 uses); and its section headings before the references.

Reading added two things the rules miss: a codename other pages use instead of the title, which we counted with series titles and the Captain Britain Corps set aside, and a team that every page linking to a character mentions. Each shuffle test uses 1,000 shuffles with seed 2805.

In-degree counts only links among these 303 pages. A character famous from British comics or television, like Miracleman or Isaiah Bradley, gets nothing for it. The trend is a correlation: links do not write words, and both could share a cause we did not measure.

Out-degree, the links a page makes, tracks length even more closely (Spearman 0.78), but a longer page has more room for links, so it partly measures length itself. PageRankA score that a node earns from the nodes linking to it, each passing on a share of its own score, so a link from a high-scoring node counts for more., which counts a link from a much-linked page for more, gives 0.71.

The names we counted come from the text alone, which lost its infoboxes, so a page can link to a character without naming it in our copy.

Pages named without a link: Spearman 0.07 with the residual, against 0.00 ± 0.06 in shuffles (\htmlClass{x-p-empirical}{p} = 0.202). The 46 hub pages: mean residual −0.21, against 0.04 for the other pages (\htmlClass{x-p-empirical}{p} = 0.008).

Each of the two explanations, hub pages and names without a link, shows at its extreme in one outlier: Brian Braddock's codename, Captain Britain, is on 14 other pages but linked from 1, and Quasar is a page for a name four characters share, with 24 incoming links.

The ten pages furthest from the line, above it first. For each, the reason we found by measuring and reading, and a passage that supports it, from the page itself or a page that names it. Four of the five below the line are minor characters whose every linking page names the same team or place.

We split each page into words: runs of letters in any alphabet, an inner apostrophe or hyphen kept, lowercased, a possessive 's removed; digits and punctuation dropped. We keep stopwords and do not lemmatise. The 303 pages hold 713,617 words.

MATTR has no trend with length, but short pages spread more because they have fewer windows to average: a standard deviation of 0.031 in the shortest quarter of pages against 0.021 in the longest. So each page gets a z-scoreHow far a value lies from what chance would give, measured in standard deviations, the typical size of chance's swings. The farther from 0, the less likely chance alone produced it. against the 30 pages nearest to it in length. Then we read the five highest and the five lowest.

The score passes its length checks. Its rank correlation with page length is 0.02, its z-scores spread 1.11 in the shortest quarter and 1.00 in the longest, and 6 of the top 10 pages are shorter than the median page of 1,218 words. With a 50-word window instead of 100, 7 of the top 10 and 8 of the bottom 10 stay in their ten (rank correlation 0.945 over all pages).

Real or boilerplate: a rare word is one found on at most 2 of the 303 pages. House phrasing is any run of 8 words found on more than 10 pages, section 2's cutoff applied to our word rule. It finds 113 such runs, led by "in american comic books published by marvel comics" on 282 pages. Both shares move with length (rank correlation 0.55 for rare words and −0.54 for house phrasing), since the house lead is a bigger slice of a short page, so each page we show is compared with the median of its 30 length neighbours. We leave out the share of a page's words used once (the hapax share): it falls as a page grows, so it cannot compare pages of different length.

Long pages also stray from random text more often: 6.6% of pages longer than the median fall outside the corpus band, against 2.0% of shorter pages. That is why each page is ranked against pages of its own length and not against the band.

The band: 2,000 random stretches of the whole corpus, every page joined in order, at each of 40 lengths (seed 2805), scored the same way. Sentences come from spaCy's rule-based sentencizer, so "Ms." and "U.S." do not end one. A page is about several characters when its first sentence says so ("Hawkeye is the name of several fictional characters"): 46 pages do. Section 6 calls them hub pages.

MATTR counts repeats, not strangeness: Coldblood wins by naming each cyborg part once, and only reading tells a list from an odd story.

A sentence past the lead of each of the top three pages, and one from the last page, quoted from the page.