Simulation Source Code for Scale-Free Network Characteristics in Complex Networks

Scale-free networks represent a classical model in complex network research, characterized primarily by their degree distribution following a power-law pattern. These networks feature a small number of highly connected hub nodes while the majority of nodes maintain relatively few connections. Simulation provides an intuitive way to demonstrate these network properties.

When implementing scale-free network simulations, the Barabási-Albert (BA) model is typically employed. The model construction process relies on two core mechanisms: network growth and preferential attachment. The implementation starts with a small initial set of nodes, where each new node connects to existing nodes with a probability proportional to their current degree. Code implementation would involve maintaining a dynamic node list and calculating connection probabilities using degree-based weighting functions.

For degree distribution analysis, we utilize log-log plots. Genuine scale-free networks exhibit distinct linear characteristics in this coordinate system, validating the power-law distribution property. In simulation diagrams, the x-axis represents node degrees while the y-axis shows the probability of corresponding degrees. The code would typically include functions for degree统计 calculation and logarithmic coordinate transformation for visualization.

Understanding scale-free network characteristics holds significant importance for studying real-world systems like internet topology, social networks, and protein interaction networks. Simulations visually demonstrate the "rich-get-richer" phenomenon where a minority of nodes attract disproportionate connections, which can be implemented through preferential attachment algorithms that bias connection probability toward higher-degree nodes.