Connected component of a hypergraph: различия между версиями

'''Connected component of a hypergraph''' — ''[[связная компонента гиперграфа]].''

Let <math>\mathcal {E} = (V, \{E_{1}, \ldots, E_{m}\})</math> be a [[hypergraph]]. A sequence <math>(E_{1}, \ldots, E_{k})</math> of distinct hyperedges is a '''[[path]]''' of length <math>\,k</math> if for all <math>\,i, \; 1 \leq i < m, \; E_{i} \cap E_{i+1} \neq \emptyset</math>. Two [[vertex|vertices]] <math>\,x \in E_{1}, \; y \in E_{k}</math> are connected (by the path <math>(E_{1}, \ldots, E_{k})</math>), and <math>\,E_{1}</math> and <math>\,E_{k}</math> 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.

 

 

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