  In many real-world networks the ability to synchronize is a key property for
its performance. Examples include power-grid, sensor, and neuron networks as
well as consensus formation. Recent work on undirected networks with diffusive
interaction revealed that improvements in the network connectivity such as
making the network more connected and homogeneous enhances synchronization.
However, real-world networks have directed and weighted connections. In such
directed networks, understanding the impact of structural changes on the
network performance remains a major challenge. Here, we show that improving the
structure of a directed network can lead to a failure in the network function.
For instance, introducing new links to reduce the minimum distance between
nodes can lead to instabilities in the synchronized motion. This
counter-intuitive effect only occurs in directed networks. Our results allow to
identify the dynamical importance of a link and thereby have a major impact on
the design and control of directed networks.
