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在[[数学中]], '''超图 hypergraph'''是有限集合的子集系统，是最一般的离散结构，在信息科学、生命科学等领域有着广泛的应用。它的一条[[graph theory|边]]可以连接任意数量的[[vertex (graph theory)|顶点]]. 相对而言，在普通图中，一条边只能连接两个顶点。形式上, 超图 <math>H</math> 是一个集合组 <math>H = (X,E)</math> 其中<math>X</math> 是一个以节点或顶点为元素的集合，即顶点集, 而 <math>E</math> 是一组非空子集，被称为边或超边.
在[[数学中]], '''超图 hypergraph'''是有限集合的子集系统，是最一般的离散结构，在信息科学、生命科学等领域有着广泛的应用。它的一条[[graph theory|边]]可以连接任意数量的[[vertex (graph theory)|顶点]]. 相对而言，在普通图中，一条边只能连接两个顶点。形式上, 超图 <math>H</math> 是一个集合组 <math>H = (X,E)</math> 其中<math>X</math> 是一个以节点或顶点为元素的集合，即顶点集, 而 <math>E</math> 是一组非空子集，被称为边或超边.
因此，若<math>\mathcal{P}(X)</math>是 <math>E</math>的幂集，则<math>E</math>是 <math>\mathcal{P}(X) \setminus\{\emptyset\}</math> 的一个子集。在<math>H</math>中，顶点集的大小被称为超图的阶数，边集的大小被称为超图的大小。
因此，若<math>\mathcal{P}(X)</math>是 <math>E</math>的幂集，则<math>X</math>是 <math>\mathcal{P}(X) \setminus\{\emptyset\}</math> 的一个子集。在<math>H</math>中，顶点集的大小被称为超图的阶数，边集的大小被称为超图的大小。
While graph edges are 2-element subsets of nodes, hyperedges are arbitrary sets of nodes, and can therefore contain an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality; a ''k-uniform hypergraph'' is a hypergraph such that all its hyperedges have size ''k''. (In other words, one such hypergraph is a collection of sets, each such set a hyperedge connecting ''k'' nodes.) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on. A hypergraph is also called a ''set system'' or a ''[[family of sets]]'' drawn from the [[universal set]].
While graph edges are 2-element subsets of nodes, hyperedges are arbitrary sets of nodes, and can therefore contain an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality; a ''k-uniform hypergraph'' is a hypergraph such that all its hyperedges have size ''k''. (In other words, one such hypergraph is a collection of sets, each such set a hyperedge connecting ''k'' nodes.) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on. A hypergraph is also called a ''set system'' or a ''[[family of sets]]'' drawn from the [[universal set]].