The diameter of weighted random graphs
Hamed Amini, Marc Lelarge
TL;DR
This paper derives a precise asymptotic expression for the weighted diameter of sparse random graphs with i.i.d. exponential edge weights, revealing how randomness affects graph distances.
Contribution
It provides a novel asymptotic formula for the weighted diameter in sparse random graphs with exponential edge weights, advancing understanding of weighted graph metrics.
Findings
Asymptotic expression for weighted diameter derived
Impact of exponential weights on graph distances quantified
Enhanced understanding of weighted shortest paths in random graphs
Abstract
In this paper we study the impact of random exponential edge weights on the distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the maximal weight of the shortest weight paths between all vertices (the weighted diameter) of sparse random graphs, when the edge weights are i.i.d. exponential random variables.
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