Granger-Faithfulness and Link Orientation in Network Reconstruction

Networked dynamic systems are often abstracted as directed graphs, where the observed system processes form vertex set and edges used to represent nonzero transfer functions. Recovering exact underlying graph structure of such a networked system, given only observational data, is challenging task. In this article, we prove that there instances networks for which any method susceptible inferring false negative or positive edges. Borrowing terminology from theory graphical models, say those unfaithful their networks. We formalize variant faithfulness systems, called Granger-faithfulness, large class networks, show Granger-unfaithful constitute Lebesgue zero-measure set. For same under Granger-faithfulness assumption, provide an algorithm reconstructs network topology, guarantees no in its output. augment topology reconstruction with orientation rules some inferred edges, consistent assumption.