  Background: Controlling global epidemics in the real world and accelerating
information propagation in the artificial world are of great significance,
which have activated an upsurge in the studies on networked spreading dynamics.
Lots of efforts have been made to understand the impacts of macroscopic
statistics (e.g., degree distribution and average distance) and mesoscopic
structures (e.g., communities and rich clubs) on spreading processes while the
microscopic elements are less concerned. In particular, roles of ties are not
yet clear to the academic community.
  Methodology/Principle Findings: Every edges is stamped by its strength that
is defined solely based on the local topology. According to a weighted
susceptible-infected-susceptible model, the steady-state infected density and
spreading speed are respectively optimized by adjusting the relationship
between edge's strength and spreading ability. Experiments on six real networks
show that the infected density is increased when strong ties are favored in the
spreading, while the speed is enhanced when weak ties are favored. Significance
of these findings is further demonstrated by comparing with a null model.
  Conclusions/Significance: Experimental results indicate that strong and weak
ties play distinguishable roles in spreading dynamics: the former enlarge the
infected density while the latter fasten the process. The proposed method
provides a quantitative way to reveal the qualitatively different roles of
ties, which could find applications in analyzing many networked dynamical
processes with multiple performance indices, such as synchronizability and
converging time in synchronization and throughput and delivering time in
transportation.
