I have a weighted graph G with approximately 75000 nodes. I would like to find subgraph G' induced on a subset of nodes, such that all edge weights in G' are greater than a given constant C and the number of nodes in this subset is maximal. In other words, I want a subgraph with this property, but it's only allowed to remove nodes with their adjecent edges, but not edges only.

Is this a know problem or reducible to one? If yes, is it tractable?