Generation Programs for SW Small-World Model and Scale-Free BA Model in Complex Networks

In complex network theory, the SW small-world model and scale-free BA model represent two fundamental network generation methodologies. The SW small-world model enhances network complexity by introducing random connections into a regular lattice structure, effectively simulating real-world network characteristics through a rewiring probability parameter. Implementation typically involves creating a regular ring lattice first, then randomly rewiring edges with a specified probability while maintaining network connectivity. The scale-free BA model emphasizes node connectivity distribution by sequentially adding new nodes that preferentially attach to existing highly-connected nodes, following the rich-get-richer mechanism. This growth process generates power-law degree distributions observed in many real-world networks. Code implementation generally requires maintaining a dynamic list of node connections, where new nodes are linked to existing nodes with probability proportional to their current degree. Both generation algorithms hold significant importance in complex network research, with the SW model capturing high clustering and short path lengths, while the BA model reproduces the hub-oriented connectivity patterns found in large-scale real networks. These models provide essential frameworks for studying network robustness, information diffusion, and topological properties.