Excitation and Measurement Patterns for the Identifiability of Directed Acyclic Graphs

The paper proves that for DAG networks, generic identifiability requires (1) every node is either excited or measured, (2) all sources are excited and all sinks are measured, and (3) all dources are excited and all dinks are measured (Theorem IV.1, with dource/dink defined in Section II) . Items (1)–(2) are inherited from a general necessary condition (Proposition II.1) . The candidate solution independently establishes the same necessity statements by constructing graph-consistent, one-parameter reparametrizations that keep M = C(I−G)^{-1}B invariant—using path-sum invariance in DAGs—thereby showing non-uniqueness whenever any condition fails. This is a different but valid proof strategy compared to the paper’s algebraic, triangular-system argument based on Lemma III.1 (relations (5)–(10)) and the ensuing need to know specific T-entries to solve for certain G-entries. We find no contradiction: both establish necessity, and neither claims sufficiency for these conditions alone.