Attack vs. random failure: how many heroes does it take to break the Marvel web?

POW! Week 2 showed our 303-character network sits closer to a Barabási–Albert graph than to a random one. BA graphs have a famous party trick: they're robust to random failure but fragile to targeted attack, because a few hubs carry a wildly disproportionate share of the paths. So this week we tested that directly on our own giant component — remove characters one at a time, in different orders, and watch how fast the network falls apart.

What we asked

Is the character whose removal fragments the network the most the same one who tops the betweenness-centrality ranking? And more broadly: if you had to design an "attack" that breaks the Marvel universe into pieces as fast as possible, is ranking by betweenness actually better than the simpler, cheaper strategy of ranking by degree — and how much worse is it to remove characters at random?

What we did

We took the undirected giant component from week 1 (277 of the 303 characters — the Morituri island and the 17 loners were dropped, since "fragmenting" an already-disconnected piece isn't meaningful) and computed betweenness centrality and degree for every node. Then we removed nodes one by one, in three different orders, and after each removal measured what fraction of the original 277 nodes was still reachable in the largest surviving piece:

• Targeted attack, by betweenness — highest betweenness first, fixed order.
• Targeted attack, by degree — highest degree first, fixed order.
• Random failure — uniform random order, averaged over 200 independent trials.

The collapse, live

Same story as the CCDF plot last week, but now it's the giant component itself falling apart. Watch how much further ahead the two targeted curves are than random failure — and how close betweenness and degree attack track each other for most of the way.

The gap is enormous. Remove the top 100 highest-betweenness characters (36% of the giant component) and only 21% of it survives as one piece; removing the top 100 by degree instead leaves 28% intact. Remove the same number of characters at random and 61% is still standing. To do half as much damage as 81 targeted removals, random failure needs 128 removals — 58% more effort for the same result. This is exactly the BA-network signature Albert, Jeong & Barabási described: a few hub characters carry a hugely disproportionate share of the network's paths, so knowing who to remove matters far more than how many you remove.

Is the top fragmenter the same as the top betweenness node?

For the single most damaging character to remove, yes: Spider-Man tops both rankings, and removing him alone only shrinks the giant component by 2.17%. That number is the real headline here — even Spider-Man is not a single point of failure. With 277 nodes and plenty of redundant paths between them, no one character can break the network; fragmentation only shows up once you strip away dozens of hubs in sequence, which is exactly what the curves above demonstrate.

But past the very top, the two rankings diverge in an interesting way. We compared each character's solo fragmentation impact (removed alone) against their betweenness and degree ranks:

Several characters near the bottom of that first table — Genis-Vell, Guardsman, Nightmask, Rockman — rank in the top 10 for fragmentation impact despite sitting far down the betweenness list (ranks 47–59) and even further down the degree list (ranks 115–249). These are classic local cut vertices: low-traffic characters whose single edge is the only thread connecting a small pendant cluster of teammates to the rest of the universe. Global betweenness barely notices them because almost no shortest paths route through their corner of the graph — but from the perspective of "how much of the network becomes unreachable if this one page disappears," they punch well above their centrality rank. Black Widow shows a milder version of the same effect: rank 8 by betweenness, but rank 2 by fragmentation impact.

What's next

The robustness curves confirm the BA-shaped story from week 2 in a much more concrete way than a degree-distribution plot: this network really does behave like a hub-and-spoke structure under stress, not a uniformly-connected one. Next week we start looking at what the hubs and the cut-vertex characters actually have in common — teams, eras, anything scrapeable from their pages.