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In mathematics, a '''random minimum spanning tree''' may be formed by assigning random weights from some distribution to the edges of an [[undirected graph]], and then constructing the [[minimum spanning tree]] of the graph.
When the given graph is a [[complete graph]] on {{mvar|n}} vertices, and the edge weights have a continuous [[Cumulative distribution function|distribution function]] whose derivative at zero is {{math|''D'' > 0}}, then the expected weight of its random minimum spanning trees is bounded by a constant, rather than growing as a function of {{mvar|n}}. More precisely, this constant tends in the limit (as {{mvar|n}} goes to infinity) to {{math|''ζ''(3)/''D''}}, where {{mvar|ζ}} is the [[Riemann zeta function]] and {{math|''ζ''(3)}} is [[Apéry's constant]]. For instance, for edge weights that are uniformly distributed on the [[unit interval]], the derivative is {{math|1=''D'' = 1}}, and the limit is just {{math|''ζ''(3)}}.<ref>{{citation
| last = Frieze | first = A. M. | authorlink = Alan M. Frieze
| doi = 10.1016/0166-218X(85)90058-7
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