Network flow analysis algorithms

Network flow analysis relies on mathematical techniques to gain knowledge about network structure in real and theoretical systems. From a two-dimensional representation of the flow of material, energy, or information in a network, indices and matrices provide non-obvious knowledge about the system. Where the indices and matrices are described in the literature, researchers rarely find an algorithm or computer code example to facilitate the inclusion of the technique into their projects. Researchers are forced to code the algorithms from scratch, which can be difficult, or obtain them from other investigators, which is time-consuming. In this paper, I describe the most popular network flow analysis indices and matrices with reference to relevant citations and supply algorithms and free software for their calculation. I also propose that researchers adopt a consistent set of primary symbolic letter designations for the indices and matrices.