这几天在看关于复杂网络的paper，其中有一个概念叫做HyperGraph,中文名译为“超图”。这个概念paper上面讲的不是很清楚，于是我去查了一下维基：

In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. Formally, a hypergraph H is a pair H = (X,E) where X is a set of elements called nodes or vertices, and E is a set of non-empty subsets of X called hyperedges or edges.

An example of a hypergraph, with X = {v1, v2, v3, v4, v5, v6, v7} and E = {e1,e2,e3,e4} ={{v1, v2, v3}, {v2,v3},{v3,v5,v6},{v4}}.

结合图，可以理解到超图就是每一个边可以包含两个以上顶点所构成的图，继续看下去：

While graph edges are pairs 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.

每个边所包含的顶点个数都是相同且为k个的，就可以被称为k阶超图。2阶超图就是我们平时所见到的图，因为我们平时的图由线条（edge，边）和点（vertice，顶点）构成，每条线都只包含两个点，所以这是符合2阶超图的定义的。

这张图一条直线或者曲线代表的是一个超边（Hyperedge）,这张图就比较清晰的证实了我的理解，确实是每一个边都只包含3个顶点。

A hypergraph is also called a set system or a family of sets drawn from the universal set X. The difference between a set system and a hypergraph is in the questions being asked. Hypergraph theory tends to concern questions similar to those of graph theory, such as connectivity and colorability, while the theory of set systems tends to ask non-graph-theoretical questions, such as those of Sperner theory.

可见，超图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。

来源：
https://blog.csdn.net/TerreHX/article/details/79433848
https://blog.csdn.net/raodotcong/article/details/6429991
https://en.wikipedia.org/wiki/Hypergraph
http://slideplayer.com/slide/4792016/