Power grids, the internet and other networks often mitigate the effects of damage using redundancy: they build in multiple routes between nodes so that if one path is knocked out by falling trees, flooding or some other disaster, another route can take over. But that approach can make them expensive to set up and maintain. The alternative is to repair networks with new links as needed, which brings the price down – although it can also mean the network is down while it happens.
As a result, engineers tend to favour redundancy for critical infrastructure like power networks, says Robert Farr of the London Institute for Mathematical Sciences.
So Farr and colleagues decided to investigate which network structures are the easiest to repair. Some repairs just restore broken links in their original position, but that may not always be possible. So the team looked at networks that require links in new locations to get up and running again. They simulated a variety of networks, linking nodes in a regular square or triangular pattern and looked at the average cost of repairing different breaks, assuming that expense increases with the length of a rebuilt link.