Three landmark network models — Erdős–Rényi random, Barabási–Albert scale-free, Watts–Strogatz small-world — with force-directed layout and degree-distribution histogram
Nodes N60
ER — prob p0.08
BA — edges m2
WS — lattice k4
WS — rewire β0.10
60
Nodes
0
Edges
0.0
Avg Degree
0.00
Clustering C
0
Giant Comp.
0
Max Degree
Erdős–Rényi G(N,p): Each pair of nodes connected with probability p.
Giant component emerges near p_c = 1/N. Degree follows Binomial → Poisson.
Barabási–Albert: Preferential attachment — new nodes link to m existing nodes
with probability ∝ degree. Creates hubs with power-law degree distribution P(k) ∝ k⁻³.
Watts–Strogatz: Start with ring lattice (k neighbours each), rewire each edge
with probability β. Low β → high clustering; high β → short average path length — the
small-world regime. Right panel shows the degree histogram
(log scale). Node size ∝ degree.