I am having some difficulty following the concept of shrinking a set of node as given in the paper On the Bottleneck Shortest Path Problem
It says:
Shrinking a set of nodes can be done in linear time. More precisely, given a set S ⊆ V of nodes of an (undirected) graph G = (V,E), one can construct in linear time another graph with nodes (V \S)$\cup${vnew} (where vnew represents the shrunken set S), where v,w ∈ V \ S are adjacent if and only if v and w are adjacent in G (in this case,the edge keeps its weight), and vnew and w ∈ V \ S are adjacent if and only if there is some v ∈ S such that v and w are adjacent in G (in which case the edge receives the biggest weight of any edge connecting S and w in G).
I am particularly confused about the last sentence of how vnew and w are adjacent. Actually I am pretty much confused about it all and any clarity would be appreciated.