  This paper addresses the problem of identifying the topology of an unknown,
weighted, directed network running a consensus dynamics. We propose a
methodology to reconstruct the network topology from the dynamic response when
the system is stimulated by a wide-sense stationary noise of unknown power
spectral density. The method is based on a node-knockout, or grounding,
procedure wherein the grounded node broadcasts zero without being eliminated
from the network. In this direction, we measure the empirical cross-power
spectral densities of the outputs between every pair of nodes for both grounded
and ungrounded consensus to reconstruct the unknown topology of the network. We
also establish that in the special cases of undirected or purely unidirectional
networks, the reconstruction does not need grounding. Finally, we extend our
results to the case of a directed network assuming a general dynamics, and
prove that the developed method can detect edges and their direction.
