Resilience and fluctuations shape primal and dual communities in spatial networks.

Both human-made and natural supply networks are built to operate reliably in changing conditions full of external stimuli. Many of these spatial networks exhibit community structures. Here, we show the existence of a second class of communities. These dual communities are based on an exceptionally strong mutual connectivity and can be found for example in leaf venation networks. We demonstrate that traditional and dual communities emerge naturally as two different phases of optimised network structures that are shaped by fluctuations and that they suppress failure spreading, which underlines their importance in understanding the shape of real-world supply networks.