What is a hypergraph
Hypergraph
What is a hypergraph?
The essential feature of a hypergraph is its hyperedge, which can connect more than two nodes (including two). In this sense, the normal graph we are familiar with is only a special case of hypergraph, and hypergraph defines a broader graph.
The mathematical definition of a hypergraph is: for a hypergraph H, there is a set of nodes V of the hypergraph and a set of E of the edges (hyperedge) of the hypergraph, then H = (V,E). Among them, each super edge e is a non-empty set of V. Generally, the number of nodes contained in e means that its degree is recorded as |e| (greater than or equal to 2).
FIG accordance super super edge to be understood that one of ordinary FIG edge connects two vertices, may be connected over a plurality of vertices FIG.
Each edge contains the same number of vertices and is k, which can be called a k-order hypergraph.
As shown in the figure above, it is an order ③ hypergraph, that is, each edge is connected to three vertices.
The meaning of hypergraph
A hypergraph can represent a situation where one edge connects multiple vertices. For example, if multiple people collaborate to produce a book, the vertex represents the author, and the edge represents the book. If only two vertices can be connected, it can only show that two authors wrote a book book.
If the vertex represents the book and the edge represents the author, similarly, the author is limited to only two books.
Therefore, personal understanding, the existence of hypergraph can express the many-to-many relationship in real life.
application
But since there is no research in this area, I don't know what specific applications are.
binary picture
Found that the more approachable
bipartite graph reference links
Personal reference summary of online information.
Hypergraph reference link 1
Hypergraph reference link 2