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In [[mathematics]], a '''hypergraph''' is a generalization of a [[Graph (discrete mathematics)|graph]] in which an [[graph theory|edge]] can join any number of [[vertex (graph theory)|vertices]]. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, a hypergraph <math>H</math> is a pair <math>H = (X,E)</math> where <math>X</math> is a set of elements called ''nodes'' or ''vertices'', and <math>E</math> is a set of non-empty subsets of <math>X</math> called ''[[hyperedges]]'' or ''edges''. Therefore, <math>E</math> is a subset of <math>\mathcal{P}(X) \setminus\{\emptyset\}</math>, where <math>\mathcal{P}(X)</math> is the [[power set]] of <math>X</math>. The size of the vertex set is called the ''order of the hypergraph'', and the size of edges set is the ''size of the hypergraph''.  

In [[mathematics]], a '''hypergraph''' is a generalization of a [[Graph (discrete mathematics)|graph]] in which an [[graph theory|edge]] can join any number of [[vertex (graph theory)|vertices]]. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, a hypergraph <math>H</math> is a pair <math>H = (X,E)</math> where <math>X</math> is a set of elements called ''nodes'' or ''vertices'', and <math>E</math> is a set of non-empty subsets of <math>X</math> called ''[[hyperedges]]'' or ''edges''. Therefore, <math>E</math> is a subset of <math>\mathcal{P}(X) \setminus\{\emptyset\}</math>, where <math>\mathcal{P}(X)</math> is the [[power set]] of <math>X</math>. The size of the vertex set is called the ''order of the hypergraph'', and the size of edges set is the ''size of the hypergraph''.  

在[[数学中]], '''超图'''是一种广义上的[[graph(discrete mathematics)|图]] ，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，被称为边或超边.  

在[[数学中]], '''超图'''是一种广义上的[[graph(discrete mathematics)|图]] ，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>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。