Removing edges from strongly connected graph

Question

Does this problem have a name?

Given a directed and strongly connected graph with edge weights, find a smallest cost set of edges such that removing that set of edges results in a graph that isn't strongly connected anymore.

Anyone know/have a solution idea? I'm thinking set this up as a network flow problem, but I'm not sure how to proceed.

Answer 1

The closest one by topic is named "Percolation Problem". You are describing an aspect of "Percolation Threshold" and "Path in Percolated Graph". There is a whole theory about it. Now you have a keyword to google.

It is interesting that your search was caused but some practical model, not the theory of graphs, paths and fractals.