We say that $E,E'\subset X$ are adjacent if $E\cap E'\neq\emptyset$. Adjacency is an equivalence relation over nonempty subsets of $X$ and we term its transitive closure by transitive adjacency. For $E_1,\ldots,E_k\subset X$ define their adjacent union by $$ \tilde\cup(E_1,\ldots,E_k):= \begin{cases} \bigcup_{i=1}^k E_i, & \text{the $(E_i)$ are transitively adjacent} \\ \emptyset, & \text{else} . \end{cases} $$

Are there standard terms for transitive adjacency and adjacent union?