Fundamental Function Program for Complex Networks

This article provides a detailed description of how to visualize Barabási-Albert (BA) and Erdős-Rényi (ER) networks. First, it's essential to understand the concepts and characteristics of these network models. The BA network is a scale-free network characterized by a large number of nodes with uneven connection distributions, typically following a power-law degree distribution. The ER network is a random network model with relatively smaller node counts where connections between nodes are established purely randomly. When generating these networks, we need to specify parameters such as the number of nodes and connection methods. Generally, programming languages like Python can be used to implement this process. For BA networks, the preferential attachment algorithm can be implemented using network libraries (e.g., NetworkX's barabasi_albert_graph function) to determine connections based on existing node degrees. For ER networks, random algorithms (e.g., NetworkX's erdos_renyi_graph function) can generate connections with specified probability parameters. Finally, we need to analyze the visualized networks through metrics like degree distribution and clustering coefficients to better understand their characteristics and applications in real-world systems.