Two methods,
one network,
different maps.

Weeks 2 and 3 asked what a single node or a single link can tell us. This week zooms out: are there groups of characters that hang together — the way X-Men, Avengers or Spider-people cluster on Wikipedia?

Modularity Q scores a proposed partition: the fraction of links that fall inside groups, minus what a degree-preserving null would expect by chance.

Q = (1/2m) sum_ij (A_ij - k_i k_j / 2m) delta(c_i, c_j)

Following the Week 4 prompt, we ask the sharper question: if we hand the same network to two different community-detection algorithms, how much do they agree, and where do they disagree?

Section 4's biggest warning: a random network's modularity is not zero, because with enough links an optimizer always finds some way to draw borders that cross fewer links than expected. We took the real 277-node, 1,421-link graph, ran 20 degree-preserving double-edge swaps (as in Week 2 and Week 3), and re-ran Louvain on each shuffle.

The real network's modularity is about 40 shuffle standard deviations above the null mean. This is the same lesson as Week 2's clustering test and Week 3's betweenness test, applied to a new statistic: Marvel's grouping is not an artifact of its degree sequence alone. But — as the course material stresses — a random network with the same size and density still reaches Q ≈ 0.25, nowhere near zero. Report modularity against its null, never on its own.

What survives: both Louvain and Infomap find far more grouping than a degree-preserving shuffle can produce (z ≈ 40). Both independently reconstruct recognizable Marvel teams: an X-Men cluster, a Spider-Verse cluster, a supernatural cluster. That convergence, on two very different objectives (modularity vs. description length), is the strongest evidence that these groups are real structure, not an artifact of one algorithm's bias.

What does not survive: the exact partition. Ten Louvain seeds already disagree with each other (NMI 0.53–0.89); Louvain and Infomap disagree even more (NMI 0.62, 40% of characters relabeled under our alignment). A single run's community list — ours included — is one sample from a landscape of similarly-scoring partitions, exactly as Section 4 warns.

We also tried the cheapest possible ground-truth check: Week 3's text-derived faction labels (X-Men / Avengers / Fantastic Four / Guardians / Spider-Man, assigned only when a character's frozen description names one). Only 8 of 277 characters qualify, and the NMI between their faction label and our Louvain community is a suspicious 1.0 — perfect agreement is what you expect from 8 data points scattered across 8 communities by chance, not evidence of anything. We report this the way the course material's "AI-drafted report" box tells us to: as a flaw to name, not a number to headline.

This is an undirected projection of Wikipedia hyperlinks, not friendship or team membership, and communities here are Louvain's or Infomap's answer to "how would you group this hyperlink graph," not Marvel canon. A hard partition also forces every high-degree crossover character — Hulk, Black Widow, Hercules — onto one side, when Section 5 and 6's overlapping methods (k-clique communities, link clustering) exist precisely because that forcing is sometimes the wrong model. That overlap-aware pass is the natural next step, not attempted here.