Note on the identification of total effect in Cluster-DAGs with cycles

In this note, we discuss the identifiability of a total effect in cluster-DAGs, allowing for cycles within the cluster-DAG (while still assuming the associated underlying DAG to be acyclic). This is presented into two key results: first, restricting the cluster-DAG to clusters containing at most four nodes; second, adapting the notion of d-separation. We provide a graphical criterion to address the identifiability problem.

@article{yvernes2025_2504.07921,
  title={ Note on the identification of total effect in Cluster-DAGs with cycles },
  author={ Clément Yvernes },
  journal={arXiv preprint arXiv:2504.07921},
  year={ 2025 }
}