  In this article we present a method to reconstruct the interconnectedness of
dynamically related stochastic processes, where the interactions are
bi-directional and the underlying topology is a tree. Our approach is based on
multivariate Wiener filtering which recovers spurious edges apart from the true
edges in the topology reconstruction. The main contribution of this work is to
show that all spurious links obtained using Wiener filtering can be eliminated
if the underlying topology is a tree based on which we present a three stage
network reconstruction procedure for trees. We illustrate the effectiveness of
the method developed by applying it on a typical distribution system of the
electric grid.
