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## Second Minimum spanning tree

Given an weighted undirected graph \( G = (V, E)\), and \(w : E \mapsto R^+\).

- Let T be
**MST**i,e minimum spanning tree of graph G. **Second MST**is a Tree T' different from T, and its weight is less than weights of all other spanning trees of G except T.

Find the **Second MST** of an input graph in ** \(O(|E|\log{|E|})\)** time.

NOTE: There is also an O(|E|) solution to this which is quite complicated.