Network Science
Three landmark network models — Erdős–Rényi random, Barabási–Albert scale-free, Watts–Strogatz small-world — with force-directed layout and degree-distribution histogram
Nodes N 60
ER — prob p 0.08
60
Nodes
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Edges
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Avg Degree
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Clustering C
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Giant Comp.
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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.