---
slug: oip-node-c11-networks-small-world-scale-free
title: Node C11: Networks / Small-World / Scale-Free
canonical: https://miscsubjects.com/a/oip-node-c11-networks-small-world-scale-free
---

# Node C11: Networks / Small-World / Scale-Free

C11 — Networks / Small-World / Scale-Free
{
  "id": "C11",
  "claim": "Connectivity in natural and social systems converges on a small set of topologies: small-world (high clustering + short path length) and scale-free (power-law degree distribution, a few hubs, many spokes).",
  "domain": ["neuroscience", "computer science", "ecology", "sociology", "molecular biology", "economics"],
  "pattern": ["small_world", "scale_free", "preferential_attachment", "hubs", "clustering"],
  "mechanism": "Small-world: start with a regular lattice and rewire a fraction p of edges randomly; at intermediate p, clustering remains high while average path length drops logarithmically. Scale-free: growth + preferential attachment ('rich get richer') produces power-law degree distribution P(k) ~ k^(-γ). Granovetter: weak ties bridge otherwise disconnected clusters.",
  "scale": "molecular → civilization",
  "claim_tier": "T1",
  "sources": [
    "Euler, L. (1736). 'Solutio problematis ad geometriam situs pertinentis.' Commentarii academiae scientiarum Petropolitanae, 8, 128-140.",
    "Watts, D.J. & Strogatz, S.H. (1998). 'Collective Dynamics of Small-World Networks.' Nature, 393, 440-442.",
    "Barabasi, A.L. & Albert, R. (1999). 'Emergence of Scaling in Random Networks.' Science, 286, 509-512.",
    "Granovetter, M.S. (1973). 'The Strength of Weak Ties.' Am. J. Soc., 78(6), 1360-1380."
  ],
  "dual": "Regular lattice (all local, no global reach) vs. random graph (no local structure, efficient paths but no clusters).",
  "falsifier": "Large adaptive networks (neural, social, metabolic, technological) that are demonstrably neither small-world nor scale-free — e.g., regular grids with no shortcuts, or homogeneous degree distributions in mature systems.",
  "rival_frame": "Network properties are statistical artifacts of growth processes, not convergent solutions to optimization problems. 'Scale-free' claims have been overstated — many real networks follow log-normal or exponential distributions; power-law fitting is often methodologically sloppy. Small-world structure is trivially expected in any spatially embedded growing network.",
  "independence_check": "HIGH. Euler (mathematics, Konigsberg, 1736) invented graph theory from a puzzle. Granovetter (sociology, Harvard, 1973) studied job-seeking networks. Watts-Strogatz (applied math, Cornell, 1998) modeled network clustering. Barabasi (physics, Notre Dame, 1999) derived preferential attachment. Four fields, four centuries, four questions, convergent finding: networks with efficient information flow look alike.",
  "pattern_type": "structural",
  "maps_to_axiom": ["A3", "A7"]
}

---

## Corpus map
- Same node, other planes: [Encyclopedia C11](/a/convergence-encyclopedia-c11) · [Inventory invariant](/a/oip-invariant-16-316-networks-small-world-scale-free)
- Edges touching C11: [convergence edge 8](/a/oip-convergence-edge-8) · [convergence edge 9](/a/oip-convergence-edge-9)
- Catalogue hub: [Public Article](/a/oip-convergence-public-article) · [Schema](/a/oip-convergence-schema)
