I have a complete, weighted, undirected graph. The edge weights are the cost of a connection between two nodes, so the minimum spanning tree is the subset of the edges with the lowest total cost such that the graph remains connected.
The MST must be connected at all times, but unfortunately the connections aren't very reliable, so I would like to add redundancy to this graph/network.
Is it possible to compute a subset of edges such that the total edge cost is minimised and edge-connectivity is over a certain minimum?