Connected component of a hypergraph

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Connected component of a hypergraphсвязная 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.

Литература

  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.