Scale-Free Networks and Small-World Networks with MATLAB Implementation

I have developed MATLAB programs implementing two types of complex networks: scale-free networks and small-world networks. The scale-free network model represents networks without specific topological rules, where node degrees follow a power-law distribution. This characteristic implies that a few hub nodes connect to numerous other nodes while most nodes maintain only limited connections. The implementation typically utilizes preferential attachment algorithms, where new nodes are more likely to connect to existing highly-connected nodes, achieved through cumulative probability distributions and random selection mechanisms in MATLAB.

Small-world networks occupy an intermediate position between regular lattices and random networks, featuring both short-range local connections and long-range global links. This unique structure enables efficient information propagation across the network. The MATLAB implementation often begins with a regular ring lattice and randomly rewires connections with a specified probability, using functions like rewire or randomization to create shortcuts while maintaining local clustering.

Programming these network models in MATLAB provides deeper insights into their structural properties and dynamic behaviors. The code implementation includes parameter configuration for network size, connection probability, and degree distribution analysis, serving as a foundation for complex network research and applications in various scientific domains.