Barabási-Albert Model: The preferential attachment mechanism generates scale-free networks
where new nodes connect to existing nodes with probability proportional to their degree k:
P(connect to node i) = k_i / Σ_j k_j. This "rich get richer" dynamics produces a power-law
degree distribution P(k) ~ k^{−3} (for m=1), creating hubs — highly connected nodes.
Scale-free networks appear in the World Wide Web, citation networks, protein interaction networks,
and social networks. The Barabási-Albert model (1999) showed that network growth + preferential
attachment naturally produces the ubiquitous power-law topology without fine-tuning. Node size
here scales with degree; color encodes age (early nodes are orange, later nodes are blue).