Critical point (network science)
In network science, the average number of connections per node, called the average degree ⟨k⟩, tells us whether a random network has a giant connected group. The critical point is at ⟨k⟩ = 1. The average degree is ⟨k⟩ = 2e/N, where e is the number of edges and N is the number of nodes.
- Subcritical: ⟨k⟩ < 1. There is no giant component; the network is made up of small clusters. If ⟨k⟩ = 0, no nodes are connected.
- Critical: ⟨k⟩ = 1. The network is at the threshold; no giant component yet.
- Supercritical: ⟨k⟩ > 1. A giant component appears, meaning a large portion of the network is connected. A complete graph has ⟨k⟩ = N − 1.
Example: speed dating. At first, ⟨k⟩ ≈ 0, so no one knows anyone. After the first round, ⟨k⟩ ≈ 1, still no giant group. After the second round, ⟨k⟩ ≈ 2, and a giant connected group forms.
This page was last edited on 3 February 2026, at 15:54 (CET).