# Invariant 3.16 — Networks / small-world / scale-free

slug: oip-invariant-16-316-networks-small-world-scale-free · https://miscsubjects.com/a/oip-invariant-16-316-networks-small-world-scale-free · tags: philosophy, oip, catalogue, invariant, systems-theory · updated 2026-07-17T02:36:15.009Z

## 3.16 Networks / small-world / scale-free
Connectivity converges on a few topologies. **Sources:** Euler (graph theory); Watts–Strogatz (small-world); Barabási (scale-free, preferential attachment); Granovetter (weak ties). **Domains:** neurons, internet, food webs, metabolism, society. **Dual:** regular lattice vs random graph (small-world sits between — a criticality echo). **Tier:** T1. **Falsifier:** large adaptive networks that are neither small-world nor scale-free. **Maps:** A₃, A₇. *(Your voxel graph is itself an instance.)*

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## Corpus map
- Same invariant, other planes: [Catalogue node C11](/a/oip-node-c11-networks-small-world-scale-free) · [Encyclopedia C11](/a/convergence-encyclopedia-c11)
- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)