  We study the relationship between dynamical properties and interaction
patterns in complex oscillator networks in the presence of noise. A striking
finding is that noise leads to a general, one-to-one correspondence between the
dynamical correlation and the connections among oscillators for a variety of
node dynamics and network structures. The universal finding enables an accurate
prediction of the full network topology based solely on measuring the dynamical
correlation. The power of the method for network inference is demonstrated by
the high success rate in identifying links for distinct dynamics on both model
and real-life networks. The method can have potential applications in various
fields due to its generality, high accuracy and efficiency.
