Nine tribes, sixty-six schools, and the philosopher holding the backbone

This week the course playground handed us a new network — 1,444 philosophers born before 1900, linked by Wikipedia citations — and four questions about community structure. We ran two community algorithms and made them fight, asked a 2,300-year-old node which tradition he belongs to, filtered the network down to its statistically irreplaceable backbone and watched the giant component come apart, and checked what the weights were doing all along.

For Weeks 1–3 we mined Marvel superheroes. This week the course's shared playground released a frozen crawl of 1,444 philosophers on English Wikipedia — everyone in the seven "list of philosophers born in …" century lists up to the end of the 19th century — with 11,135 directed article-to-article links, each carrying its count of repeated links as a weight. Each philosopher also carries metadata: the era list they appear in and any of Wikipedia's subfield lists they're also on (metaphysicians, logicians, ethicists …).

Everything below runs on the same preprocessing: treat links as mutual (a citation made in either direction connects two thinkers), sum the two directions' weights, and work on the giant component of that undirected weighted network — 1,374 philosophers and 9,139 edges. The remaining 70 sit outside it, unanchored. Every number and figure was computed once, offline, in analysis/build_week4.py (NetworkX, python-igraph's Infomap, scikit-learn for NMI) and frozen into data/philosophers/week4_summary.json — the browser only looks numbers up and draws them.

• Giant component1,374 of 1,444
• Louvain → communities9
• Infomap → modules67
• NMI between them0.613

Same network, two objective functions, two histories. Louvain maximizes modularity and finds 9 communities of 4–283 philosophers. Infomap minimizes the map equation and finds 67 modules — its ten largest are shown right, the remaining 57 catch the long tail of small, very internally-coherent schools. Their agreement (NMI = 0.613) is real but partial, and the disagreements are exactly where the history of philosophy gets interesting.

Look at what each method's groups are. Louvain's nine communities are, almost without exception, centuries:

• 283 members, 215 of them from the 19th century — Meinong, Schopenhauer, Freud, Bruno Bauer, Kierkegaard
• 251 members, mostly 17th–18th — Descartes, Newton, Spinoza, Adam Smith, Comte
• 211 members, mostly 11th–14th and 1st–10th — Al-Farabi, Al-Ghazali, Al-Kindi, Proclus, Alexander of Aphrodisias
• 158 members, the Latin Christian middle — Augustine, Boethius, Aquinas, Ockham, Erasmus
• 149 members, mostly BC — Plato, Socrates, Heraclitus, the Stoics, Plotinus
• 147 members, almost all 19th — Russell, Frege, Peirce, James, Dewey, Carnap
• 96, 75 and 4 stragglers — the last containing an entire Chinese cluster (Confucius, Laozi, Zhu Xi)

That reading is visible in the metadata: Louvain's partition aligns with the century-bucket era labels at purity 0.576 — nearly six philosophers in ten sit in a community whose majority era matches their own. Infomap hits 0.686 — but it reaches that by doing the opposite thing: instead of grouping by century, its fine modules purify each era from inside. Its modules are recognizably schools:

• 36 members, Scottish Enlightenment — Hume, Adam Smith, George Berkeley
• 30 members, Hegelian left — Marx, Engels, Bruno Bauer, Lenin
• 29 members, pragmatism — William James, Dewey, Peirce
• 28 members, the phenomenology seedbed — Husserl, Brentano
• 52 members, the falsafa — Averroes, Avicenna, Al-Farabi, Al-Ghazali
• 143 members, the one big mixed block, which we return to below — Kant, Schopenhauer, Spinoza, Durkheim

Aristotle is the most-connected node in the network: 300 link-partners in the giant component (521 counting weight). Louvain files him under the 211-member "ancient & Islamic commentary" community. That is a textbook answer. His links tell a different one:

• 111 of his 300 neighbours sit in his own community — Alexander of Aphrodisias, Simplicius, Philoponus, Themistius, Al-Farabi, Avicenna, Averroes: the commentators
• 60 point into the ancient Greek isle — Plato, Socrates, the Stoics, Diogenes Laertius, Epicurus
• 45 into the Latin Christian world — Augustine, Boethius, Aquinas, Erasmus
• 34 into early modernity — Descartes, Newton, J.S. Mill, Comte
• 31 into the German century — Kant, Hegel, Husserl, Brentano, Heidegger, Lenin
• 17 into the analytic/pragmatist camp — Russell, Frege, Peirce, Dewey
• 2 into the Chinese cluster

His links touch seven of Louvain's nine communities. No other node in the network does that. The figure below draws every one of those 300 links (gray = links between his neighbours) coloured by the community of the philosopher on the other end.

For a second, sharper instrument we ran k-clique communities over the giant component and collected every k-clique community (k = 5) that contains him. Six survive, and one of them is a 467-node blob that simply says "Aristotle is, overlappingly, friends with more or less everyone." The other five are the money result — each of them is a tradition hand him down, and no two are the same tradition:

• The 12th-century translation effort (9) — Calcidius, Boethius, Adelard of Bath, William of Conches, Thierry of Chartres, Anselm, John of Salisbury: the portal through which Aristotle (and via him Plato) reentered Latin Europe
• Medieval logic (8) — Boethius, Albert of Saxony, Buridan, Oresme, Bradwardine, Marsilius of Inghen, Ockham
• Persian falsafa (6) — Al-Farabi, Avicenna, Mir Damad, Mulla Sadra, Jamal al-Din al-Afghani
• Renaissance heterodoxy (5) — Aquinas, Averroes, Pomponazzi, Vanini
• Phenomenology (5) — Husserl, Heidegger, Scheler, Nicolai Hartmann

Weights are counts of repeated links — but which edges are carrying real weight and which are just noise? The disparity filter (Serrano, Boguñá & Vespignani, 2009) asks, for every node, whether its share p_ij of its total outgoing link weight concentrated on one neighbour could plausibly arise if its strength were spread uniformly at random over its k links. The tail probability is α_ij = (1 − p_ij)^k−1; keep an edge if it is significant from either endpoint at level α, and watch what survives.

The explorable below lets you run the filter yourself. Drag the α slider (log scale) to tighten the significance test, and watch the network — all 1,374 philosophers, a frozen precomputed layout — lose its edges one by one. Two things to find: the exact α at which the giant component first spans less than half the network, and the philosopher whose links are still carrying everything as it comes apart. Spoilers live in the reveal panel below — try the quests first.

All of the community machinery so far used the weights. Throw them away — treat every repeated and every single link identically — and Louvain finds 8 communities instead of 9. Between the weighted and unweighted partitions, NMI = 0.650: substantial agreement, far from identity. And 1,217 of the 1,374 philosophers (88.6%) end up in a different Louvain community number when the weights vanish — though part of that is communities being renumbered, which is why the figure below shows the actual pairwise membership flows:

The pattern in the moves is not random: weights amplify polarization within traditions. The clearest example is the Islamic golden age. Unweighted, Louvain puts Al-Farabi, Al-Ghazali and Avicenna together in one 88-member community; weighted, the falsafa keep their 52-member module and the ancient commentary tradition (Al-Kindi, Alexander of Aphrodisias, Proclus) becomes a distinct partner — same overall neighbourhood, finer subdivisions. Similarly, the 19th-century block splits by persuasion when weights return: with the weights on, Aristotle's neighbours split cleanly by citation habit: the falsafa (Al-Farabi, Al-Ghazali, Avicenna, Averroes) sit with Al-Kindi and Alexander of Aphrodisias and Proclus in one 211-member commentary mega-community, and the enormous Plato–Plotinus BC-and-commentary soup unweights apart

We asked whether two community algorithms tell the same history (they don't: NMI 0.613, 9 tribes vs 67 schools, and the disagreement is modularity's resolution limit working exactly as theory says); which tradition Aristotle is really in (all of them: his 300 links touch seven of nine communities, and his k-clique communities span the translation movement, medieval logic, falsafa, Renaissance heterodoxy and phenomenology); where the statistically irreplaceable backbone is (critical α ≈ 0.16, with Aristotle carrying the most surviving backbone links at every stage until the very last edges and Heraclitus→Plutarch the final link); and whether the weights change the story (NMI 0.650 — the broad strokes survive, but the weights re-draw the lines inside eras along citation lines).

What surprised us most was the ending of the backbone experiment. We expected the final survivors to be a hub — Kant, maybe, whose links to 20th-century textbooks are everywhere. Instead the network's very last standing structure is two islands: a 19th-century Hegel-to-Marx cell, and a four-node cluster of Aristotle, Heraclitus, Plutarch and a 14th-century Oxford scholastic — a late-antique doxography book club, outliving every modern school. The disparity filter doesn't find who is famous. It reports who certain other people could not stop citing.

Caveats: this is a Wikipedia link network, which is a measure of present-day attention as much as historical influence — 20th-century analytic philosophers central to that attention economy are only partially represented here, since the roster is capped at pre-1900 birth years. And α_ij is computed per node versus that node's own link strength, so ties between low-degree nodes (our ever-present leaf triangles near the end) pass the significance bar trivially — which is why we read the backbone's final fragments rather than its last stragglers.

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