  Spreading phenomena essentially underlie the dynamics of various natural and
technological networked systems, yet how spatiotemporal propagation patterns
emerge from such networks remains largely unknown. Here we propose a novel
approach that reveals universal features determining the spreading dynamics in
diffusively coupled networks and disentangles them from factors that are system
specific. In particular, we first analytically identify a purely topological
factor encoding the interaction structure and strength, and second, numerically
estimate a master function characterizing the universal scaling of the
perturbation arrival times across topologically different networks. The
proposed approach thereby provides intuitive insights into complex propagation
patterns as well as accurate predictions for the perturbation arrival times.
The approach readily generalizes to a wide range of networked systems with
diffusive couplings and may contribute to assess the risks of transient
influences of ubiquitous perturbations in real-world systems.
