Edge Flows in the Complete Random-Lengths Network
arXiv:0708.0555
Abstract
Consider the complete n-vertex graph whose edge-lengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along the shortest path. Each edge gets some random total flow. In the $n \to \infty$ limit we find explicitly the empirical distribution of these edge-flows, suitably normalized.
38 pages, 4 figures