Should I Buy It?
Every Hollywood actor is 6 films away from Kevin Bacon. In a network of 300 million people, 6 links are enough to connect two strangers. Not 60, not 600 — 6. That’s the “small world” property: a few hyperconnected nodes collapse distances across the entire graph.
Origin
Stanley Milgram (1967) sent letters to strangers in Nebraska with instructions to get them to a target in Boston — only through direct acquaintances. Average result: 6 intermediaries. Hence “Six Degrees of Separation.”
Watts & Strogatz formalized in 1998: a network is “small world” if its diameter (maximum distance between two nodes) grows logarithmically with network size, not linearly.
Why it works: weak ties and hubs
Weak ties — Granovetter (1973): the most useful links for information aren’t close friends (strong ties) but distant acquaintances (weak ties) — they connect different clusters.
Hubs — Barabási & Albert (1999): in most real networks, a few nodes are hyperconnected. These hubs drastically reduce the average distance between all other nodes.
Examples: Kevin Bacon in the actor network. Wikipedia in the knowledge network (every article is ~4-5 clicks from any other).
Application to a concept graph
In a well-connected graph of 200 concepts, any concept should be reachable from any other in ≤5 links — if the graph is well structured.
Conceptual hubs are foundational concepts with high PageRank: they appear in many different files and serve as shortcuts. In this graph: Permissionless Leverage, Ego Depletion, Specific Knowledge.
The real value: two concepts from very different topics can be 2-3 links from each other via intermediate hubs — a non-obvious connection that generates an original insight.
“The most interesting intellectual work happens at discipline boundaries — where two concept graphs touch.”
Rules to maintain the small world property
Neither too few links (disconnected graph) nor too many (noise, no information):
- Minimum: ~log(N) links per node (at 200 concepts ≈ 7-8 links)
- Recommended maximum: 10-15 links (most semantically significant)
- “Hub” threshold: if a concept has >20 links, it’s a foundational hub
When adding a new concept: compare with direct neighbors of the closest concepts (BFS level 1-2), stop at depth 3. You find 80% of links by exploring 20% of nodes.
Sources
- Watts, D. J. & Strogatz, S. H. (1998). “Collective dynamics of ‘small-world’ networks.” Nature, 393, 440–442.
- Milgram, S. (1967). “The Small World Problem.” Psychology Today, 1(1), 61–67.
- Barabási, A.-L. & Albert, R. (1999). “Emergence of Scaling in Random Networks.” Science, 286(5439), 509–512.
- Granovetter, M. (1973). “The Strength of Weak Ties.” American Journal of Sociology, 78(6), 1360–1380.
- Barabási, A.-L. (2002). Linked: The New Science of Networks.