Triadic Closure 2D — Force-Directed Network Growth

Network Growth

Triadic closure probability p 0.75

New links per joining node m 2

Growth rate 2.0 nodes/s

Network size cap 60 nodes

Live Metrics

Nodes N

Edges E

Avg. degree ⟨k⟩

0.00

Avg. clustering C̄

0.000

Random-graph baseline

0.000

Graph diameter (exact)

Node colour scales with degree (dark → warm = local hub). This is the 2D companion: instead of an orbiting 3D camera, a genuine 2D spring-repulsion layout settles the graph in the plane, with live clustering-history and degree-distribution plots below.

How it works

This is the Holme–Kim model (Holme & Kim, 2002) — a growth process that reproduces the one property plain random-attachment graphs get wrong about real social networks: your friends tend to know each other. It's the same growth mathematics as the 3D version of this simulator, paired here with a genuinely different, independently-computed 2D mechanic: a planar spring-repulsion force layout (not a flattened 3D scene) plus two live statistical plots that have no 3D equivalent.

Each new node adds m edges:
 1st edge  → a uniformly random existing node u
 edge i>1  → with probability p: a random neighbour of the
             previously-attached node (closes a triangle)
             else: a uniformly random existing node

The triadic-closure step is exactly "friend of a friend": if you just connected to person A, there's a chance your next connection is one of A's existing contacts, not a stranger. That single rule is what pushes local clustering far above what pure random attachment produces.

Local clustering:  Cᵢ = 2·Tᵢ / (kᵢ(kᵢ−1))
  Tᵢ = triangles through node i,  kᵢ = degree of node i
Network average:   C̄ = (1/N) Σᵢ Cᵢ
Random-graph (Erdős–Rényi) expectation for the same size: C ≈ ⟨k⟩ / N

2D layout physics (independent of the 3D version's 3D-vector layout):
  repulsion Fᵢⱼ = k_r / d²           (Coulomb-like, planar)
  spring    Fᵢⱼ = k_s · (d − L₀)      (Hooke's law along each edge)
  + soft boundary containment force keeping every node on-canvas
  + velocity damping each step until the layout reaches equilibrium

p = 0 — pure random attachment, no preference for closing triangles; C̄ stays close to the random-graph baseline.
p → 1 — nearly every extra edge closes a triangle; C̄ climbs sharply above the baseline while the network keeps growing at the same rate, matching what's measured in real friendship and collaboration graphs.
m — more edges per arriving node means a denser, more connected graph overall (higher ⟨k⟩), independent of the clustering effect.
Graph diameter — the longest shortest path between any two nodes, recomputed exactly by breadth-first search from every node each time the graph changes (cheap at this scale); triadic closure tends to keep it small even as clustering rises, the "small-world" signature of real social graphs.

Edge (social tie) Hub (high degree)

clustering history —

degree distribution —