---- > [!definition] Definition. ([[hypergraph]]) > A **hypergraph** (or **hypernetwork**) is a generalization of a [[network|graph]] in which an edge can join any number of nodes. > Explicitly, an **(undirected) hypergraph** is a pair $(V, H)$, where $H \subset \mathcal{P}(V)$ [[power set|is]] a collection of subsets of $V$. > Cf. the discussion in [[binary relation]], a [[hypergraph]] carries a strict [[poset|partial order]] obtained by declaring all nodes incomparable, all hyperedges incomparable, and $v<h$ if the node $v$ belongs to the hyperedge $h$. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```