# The Min Mean-Weight Cycle in a Random Network

@article{Mathieu2013TheMM,
title={The Min Mean-Weight Cycle in a Random Network},
author={Claire Mathieu and David Bruce Wilson},
journal={Combinatorics, Probability and Computing},
year={2013},
volume={22},
pages={763 - 782}
}
• Published 19 January 2012
• Mathematics
• Combinatorics, Probability and Computing
The mean weight of a cycle in an edge-weighted graph is the sum of the cycle's edge weights divided by the cycle's length. We study the minimum mean-weight cycle on the complete graph on n vertices, with random i.i.d. edge weights drawn from an exponential distribution with mean 1. We show that the probability of the min mean weight being at most c/n tends to a limiting function of c which is analytic for c ≤ 1/e, discontinuous at c = 1/e, and equal to 1 for c > 1/e. We further show that if the…
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