Advanced Graph Theory

• Hypergraphs

Hypergraphs

A hypergraph $H(V,E)$ is a generation of a graph where each edge can contain any number of vertices. Here, $V$ is the set of vertices, and $E \subseteq \mathbf{P}(V) \setminus \emptyset$ is the set of hyperedges, where $\mathbf{P}(V)$ is the power set of $V$ (i.e., the set of all subset of $V$). If all hyperedge has the same size $k$, then the hypergraph is called as $k$-uniform hypergraph.