Edge flows in the complete random-lengths network

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 → ∞ limit we find explicitly the empirical distribution of these edge-flows, suitably normalized. Key words. Flow, percolation tree, random graph, random network. MSC2000 subject classification. 60C05, 05C80, 90B15. ∗ Research supported by N.S.F. Grant DMS0704159 1 

• Type: Journal
• Year: 2010
• Where: RSA
• Authors: David J. Aldous, Shankar Bhamidi
• Keywords: Complete N-vertex Graph, Random, Random Variables, RSA 2010