  Inferring network topology from dynamical observations is a fundamental
problem pervading research on complex systems. Here, we present a simple,
direct method to infer the structural connection topology of a network, given
an observation of one collective dynamical trajectory. The general theoretical
framework is applicable to arbitrary network dynamical systems described by
ordinary differential equations. No interference (external driving) is required
and the type of dynamics is not restricted in any way. In particular, the
observed dynamics may be arbitrarily complex; stationary, invariant or
transient; synchronous or asynchronous and chaotic or periodic. Presupposing a
knowledge of the functional form of the dynamical units and of the coupling
functions between them, we present an analytical solution to the inverse
problem of finding the network topology. Robust reconstruction is achieved in
any sufficiently long generic observation of the system. We extend our method
to simultaneously reconstruct both the entire network topology and all
parameters appearing linear in the system's equations of motion. Reconstruction
of network topology and system parameters is viable even in the presence of
substantial external noise.
