Calculation of Average Path Length in Complex Networks

The calculation of average path length in complex networks serves as a fundamental metric in network theory, quantifying the overall efficiency of information transmission between nodes. To compute this metric, one typically employs shortest-path algorithms (such as Dijkstra's or Floyd-Warshall) to determine the minimum distance between all node pairs in the network. While computationally intensive for large-scale networks, this process can be efficiently implemented using MATLAB's built-in graph functions. The MATLAB source code for complex network average path calculation utilizes key functions like graph() to create network objects and distances() to compute shortest paths between nodes. Available through online repositories, this code can be customized to handle directed/undirected networks, weighted edges, or disconnected components through proper algorithm selection and connectivity checks. The implementation typically involves: 1) constructing an adjacency matrix representation, 2) applying path-finding algorithms to all node pairs, 3) averaging valid path lengths while excluding infinite distances (disconnected nodes), and 4) normalizing results for network size comparison.