Scale-Free Network Implementation Using Roulette Wheel Selection Algorithm

Scale-free networks represent a fundamental concept in complex network research, characterized by degree distributions following power-law patterns where a few hub nodes possess numerous connections while most nodes have limited links. This network structure prevails across real-world systems including the internet, social networks, and biological networks.

The Roulette Wheel Selection algorithm plays a crucial role in generating scale-free networks, particularly within preferential attachment models. This method simulates roulette wheel mechanics to select existing nodes for new connections, favoring highly-connected nodes to drive the network toward power-law degree distributions.

Implementation typically involves these key programming steps: Network Initialization: Start with a small core network (e.g., a few interconnected seed nodes). Node Addition: Iteratively introduce new nodes, each with a predetermined number of connections. Preferential Selection: Apply roulette wheel selection where connection probabilities are weighted by existing nodes' degrees. Higher-degree nodes receive proportionally larger probability slices on the virtual roulette wheel. Iterative Expansion: Repeat the process through multiple iterations to form mature scale-free networks.

The algorithm ensures the "rich-get-richer" phenomenon where highly-connected nodes attract new links more frequently, which constitutes a defining characteristic of scale-free networks. Code implementation would typically involve maintaining degree arrays, calculating cumulative probabilities, and using random number generation for node selection.