Week 2: Marvel Transit Authority
02805 Social graphs & interactions · Week 2 · Models & null models
Three famous models audition for the part of the Marvel network. Each one nails a scene and fluffs the rest. Then we stop asking which model looks right and start asking what chance could have produced.
The part
The role is the connected core of the Marvel Wikipedia snapshot: every article that can reach every other by following links in either direction. These are the numbers a candidate has to reproduce.
Network science began by asking whether a simple mechanism could manufacture a structure like this. Three attempts follow, in the order the field made them, each fixing what the last one missed.
The auditions
Every candidate is built to the same size as Marvel and handed the same three scenes to play: short paths, clustering, and hubs. Pick one and watch it try.
| Network | Mechanism | Short paths ±20% | Clustering ±25% | Hubs ±40% |
|---|
One seed per model, one run · not an average over many draws.
The tail
The share of articles with at least k links, on log axes, with no binning. A heavy tail runs straight and far. A coin-flip tail falls off a cliff. This is a visual read, not a fitted power law: no distribution was fit to these tails.
The turn
No model wins, so the question changes. Instead of building a network that looks like Marvel, keep Marvel's own degrees exactly and scramble only who is wired to whom. Swap the ends of two links at a time, over and over. Everyone keeps their link count. The neighbourhoods dissolve.
Clustering now
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0 swaps
Every article keeps its exact number of links.
One shuffle proves nothing, so we ran many and kept the score. Marvel's real value sits against the whole distribution of what scrambling produces.
| Measurement | Marvel | Null mean | Null SD | z | p |
|---|
The negative
Draw a character at random, then one of their neighbours at random. The neighbour usually has more links, because popular articles sit in many neighbour lists. That is the friendship paradox, and it is real here. Pull the handle a few times and watch it appear.
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Press draw
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their random neighbour
The handle measures single draws: one character, one of their neighbours. The 87.4% quoted below is the other common form, comparing each article with the average of all its neighbours. Both are the friendship paradox, and they are not the same number: the neighbour-average form below matches what the shuffle predicts, but the single-draw form here is slightly weaker than the shuffle predicts.
Receipts
Tolerances on the scorecard are our choice and are printed in the column headings; the raw values sit beside every verdict so you can apply your own. The live rig is a feel for the mechanism and is not the source of any statistic. Nothing here says why the links exist, only what chance alone would and would not produce.