Complex Network Generation with Power Law Distribution

A complex network is a network structure composed of a large number of nodes and intricate connections. The characteristic feature of this network structure is the diverse connection patterns between nodes, which form complex topological patterns. These patterns can be represented as network matrices or adjacency matrices. Power law distribution is a common pattern where a few nodes exhibit very high connectivity degrees while most nodes are connected to only a few others. This distribution can be implemented using algorithms like the Barabási-Albert model, where new nodes preferentially attach to existing highly-connected nodes. Complex networks are widely used to study real-world systems such as social networks, internet infrastructures, and biological networks. In MATLAB implementation, one can use graph theory toolbox functions like graph and adjacency to create and analyze these networks, while power law degree distribution can be achieved through configuration model algorithms or preferential attachment mechanisms.