Calculating Average Path Length, Degree Distribution, and Clustering Coefficient for Complex Networks

Complex network analysis is a crucial method for studying structural properties of networks, where average path length, degree distribution, and clustering coefficient are three fundamental metrics. Calculating these metrics in MATLAB enables researchers to efficiently understand both global and local network characteristics. Average path length represents the mean shortest path distance between any two nodes in the network. In MATLAB implementation, this can be computed by first constructing the adjacency matrix of the network, then using graph theory functions like graphallshortestpaths or distances to calculate shortest paths between all node pairs, and finally taking the average of these values. A smaller average path length indicates higher information transmission efficiency in the network. Degree distribution describes the probability distribution of node degrees throughout the network. The computation involves counting connections for each node and analyzing the distribution pattern of these degree values. In MATLAB, node degrees can be obtained by calculating row sums or column sums of the adjacency matrix using sum(A,1) or sum(A,2), followed by statistical analysis using functions like histcounts or degreeDistribution to examine distribution characteristics. The shape of degree distribution can reveal whether the network follows random network, scale-free network, or other topological patterns. Clustering coefficient measures the network's clustering tendency, indicating the likelihood that neighbors of a node are also connected to each other. Local clustering coefficient calculates connection density among a node's neighbors, while global clustering coefficient averages all local coefficients. MATLAB provides efficient computation through triangle counting methods using functions like clustering_coef_bu or transitivity. High clustering coefficients typically suggest the presence of community structure within the network.