For DAGs with a unique LCA for every leaf subset of allowed size, the clusters that survive the simplification operator are exactly those that are inclusion-minimal for some allowed subset, and the deleted vertex set is unique.
Adv Data Anal Classif 3:189–204, DOI 10.1007/ s11634-009-0046-7
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Characterizing and Transforming DAGs within the I-LCA Framework
For DAGs with a unique LCA for every leaf subset of allowed size, the clusters that survive the simplification operator are exactly those that are inclusion-minimal for some allowed subset, and the deleted vertex set is unique.