Selected border case
Social Graphs & Interactions
Communities / weights / stability
The weekly philosophy review
The weight
of ideas
Does counting repeated links rewrite the history of philosophy—or make its existing schools harder to erase?
The answer is both, but mostly the latter. Weighted and unweighted Louvain agree at — NMI. Yet real weights preserve the unweighted map better than shuffled weights do. Strong links move borders, while reinforcing the large traditions already visible in topology.
- philosophers
- —
- article pairs
- —
- communities
- — → —
- partition agreement
- —
Figure 1 / the great rearrangement
Follow 1,374 thinkers across two maps.
Left: every article pair counts once. Right: repeated links count repeatedly. Each ribbon is a flow of philosophers; hover a block or ribbon to isolate it. Names come from each group’s strongest hub, not from historical ground truth.
Unweighted topology
Weighted attention
Figure 2 / border desk
Who feels the weights most?
These are high-degree philosophers whose two communities overlap least. Select a name to inspect the move. “Overlap” is the Jaccard similarity between that philosopher’s two groups.
Figure 3 / doubt before declaration
A score is not a structure.
Stability across seeds
Ten runs per representation produce 45 pairwise comparisons. Near-equal modularity does not imply the same partition.
Shuffle the weights
We permuted the observed weights over the same links 30 times. This keeps topology and the weight distribution, but destroys which pairs are repeatedly linked.
How to read this issue
One network, two questions.
- Representation
- A node is a pre-1900 philosopher’s Wikipedia article. An undirected edge means either article links to the other in its prose. Weight is the sum of links in both directions. We analyze the 1,374-node giant component.
- Community method
- NetworkX Louvain, seed 0 for the displayed partitions. The unweighted run treats every pair equally; the weighted run uses repeated article links. Group names are labels based on the highest-degree or highest-strength member—not discovered schools.
- Comparison
- NMI compares partitions (1 identical, 0 independent). Weighted and unweighted modularity are shown separately and never treated as directly comparable because they score different data.
- Null and limit
- The weight-permutation null asks whether the placement of strong ties matters. It does not preserve each philosopher’s strength, so it is a targeted test of weight placement, not a universal weighted-network null.
- Human check before publishing
- Open one border case, inspect its strongest links in the frozen TSV, and read the linked Wikipedia passages. Record whether the proposed move has historical meaning or is an editorial artifact.
- Reproduce
uv run analyse_week4.pyrebuilds the evidence file.