Connected component of a hypergraph

Connected component of a hypergraph — связная компонента гиперграфа.

Let $\mathcal {E} = (V, \{E_{1}, \ldots, E_{m}\})$ be a hypergraph. A sequence $(E_{1}, \ldots, E_{k})$ of distinct hyperedges is a path of length $\,k$ if for all $\,i, \; 1 \leq i < m, \; E_{i} \cap E_{i+1} \neq \emptyset$ . Two vertices $\,x \in E_{1}, \; y \in E_{k}$ are connected (by the path $(E_{1}, \ldots, E_{k})$ ), and $\,E_{1}$ and $\,E_{k}$ are also connected. A set of hyperedges is connected if every pair of hyperedges in the set is connected. A connected component of a hypergraph is a maximal connected set of hyperedges.