Snowflake-like networks (left) and the loops from which they were built (Image: Robert S. Farr, John L. Harer,3, and Thomas M. A. Fink)

Networks shaped like delicate snowflakes are the ones that are easiest to fix when disaster strikes.

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.

Loopy links

They found the best networks are made from partial loops around the units of the grid, with exactly one side of each loop missing. All of these partial loops link together, back to a central source. These have a low repair cost because if a link breaks, the repair simply involves adding back the missing side of a loop. What’s more, they are resistant to multiple breaks over time, as each repair preserves the network’s fundamental design.

These networks have three levels of hierarchy – major arms sprouting from a central hub that branch and then branch again, but no further. When drawn, they look remarkably like snowflakes, which have a similar branching structure.

Real-world networks are rarely an exact grid, so the snowflake pattern is an idealised version of one that could exist in practice and be fairly easy to repair, perhaps with just two levels of hierarchy, says Farr. Now he plans to look at how the idea might actually be implemented for power or communication networks. “That is the sort of network that people are worried about damage happening and they are essential to our infrastructure,” he says.

Sean Wilkinson of Newcastle University, UK, says such designs might be useful for networks that could suffer unpredictable damage due to future climate change. “I think this idea could help to design networks that are more readily adaptable, rather than easily reparable.”

Journal reference: Physical Review Letters, DOI: 10.1103/PhysRevLett.113.138701