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Graphs are commonly used to represent and visualize causal relations. For a
small number of variables, this approach provides a succinct and clear view of
the scenario at hand. As the number of variables under study increases, the
graphical approach may become impractical, and the clarity of the
representation is lost. Clustering of variables is a natural way to reduce the
size of the causal diagram, but it may erroneously change the essential
properties of the causal relations if implemented arbitrarily. We define a
specific type of cluster, called transit cluster, that is guaranteed to
preserve the identifiability properties of causal effects under certain
conditions. We provide a sound and complete algorithm for finding all transit
clusters in a given graph and demonstrate how clustering can simplify the
identification of causal effects. We also study the inverse problem, where one
starts with a clustered graph and looks for extended graphs where the
identifiability properties of causal effects remain unchanged. We show that
this kind of structural robustness is closely related to transit clusters.
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