The similarity cascade

Week 1 built a network out of links. Week 6 built similarity out of language. Question three from the 6.11 list: who is textually close but structurally far away? Instead of rank lists, we draw both networks on top of each other and classify every edge — the disagreements light up in red.

Both layers live over the same 303 characters, colored by their week-4 Louvain community and sized by in-degree:

Every edge is then put in one of three classes:

• both — linked on Wikipedia and textually close: 782 edges. The two lenses agree.
• dashed gray — a structural link the text doesn't rank in its top-k: 652 edges. Weak ties the vector doesn't reward.
• text-only (red) — textually close but structurally unrelated: the cascade, 1,474 edges. Where representation and structure part ways.

Start in all characters with just text-only visible and the network dissolves into a red halo around every community; re-add both and the structural skeleton reappears inside each halo. Shots worth trying:

Not every red edge is scandal. Zooming into the picture, the 1,474 text-only edges sort into three familiar families — exactly the ones week 6 taught us to diagnose:

1. Surname matches. storm links Storm to the Human Torch; frost ties Emma Frost ↔ Jack Frost — the #1 unlinked pair of the main week-6 post, cos = 0.44.
2. Unlinked teammates. The Strikeforce: Morituri cluster sits as its own community with text everywhere and links only inbound: 606 of the 1,817 directed text-only edges (33%) join characters inside the same Louvain community — the network already knows they belong together; the link layer just never wired the pages up.
3. Shared boilerplate. The she/her pronoun edges that made Jean Grey, Scarlet Witch and She-Hulk each other's textual mirrors — the same artifact the course page warned about with the and Marvel.

Switch the representation to raw counts and the collapse is dramatic: the textual layer grows to 2,712 pairs but agreement with structure falls from 782 to just 418 — stopwords generate similarity the real network never needed. That is the same 1.9 → 4.0 jump as rank lists — now visible as the ring between the text halo and the structural skeleton.

The textual layer is still only each page's top-k — weaker true similarities never enter, so structural-only under states how much structure the text misses (also note these are cosine ranks, not statistical tests). And a classified edge is a hypothesis, not a verdict: the sentence drawer in the main week-6 explorable is where that verdict gets made.

1. 2The Marvel map — the science ↔ magic / body ↔ mind axis playground, with scattertext-style term contrasts per community.
2. 3One-character deep dives — a zoomable fingerprint explorer: TF-IDF, topic mixture and embedding neighborhood around a single page.