Line graph of a hypergraph

Summary

In graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph $H$, denoted $L(H)$, is the graph whose vertex set is the set of the hyperedges of $H$, with two vertices adjacent in $L(H)$ when their corresponding hyperedges have a nonempty intersection in $H$. In other words, $L(H)$ is the intersection graph of a family of finite sets. It is a generalization of the line graph of a graph.