Robust Networks

Here we define a robust network to be a connected network that stays connected after a arbitrary link is removed. The minimal robust network connecting a set of nodes is a Hamiltonian cycle. Further, a robust network is called reduced if it can not stay robust after any link is removed. A robust network may contain multiple reduced robust networks. And reduced robust networks may be obtained by removing links from robust networks. It's a open problem to computationally characterize robust networks, and reduced robust networks. Not every robust network can be reduced to the minimal robust network because not every robust network contains a Hamiltonian cycle. It's another open problem to computationally find reduced robust networks contained in arbitrary robust networks.