---
tag: Z9A4ZHMF4G
kind: concept
name: Line graph of a hypergraph
aliases: [intersection-line-graphs-of-hypergraphs, line-graphs-of-hypergraphs, linear-hypergraphs]
sources:
  - wikipedia: en:16181442@r1352725289
    locator: Line graph of a hypergraph
    note: adopted
    mention: wikipedia://en/16181442
    sections: [Summary]
same_as:
  wikidata: Q6553253
  wikipedia: Line graph of a hypergraph
inventory: [C46XQT5VWM]
---

## Summary

In graph theory, particularly in the theory of hypergraphs, the **line graph of a hypergraph** $H$, denoted $L(H)$, is the [[graph|00C0BR7D7H]] whose vertex set is the [[set|0BSJ7RQ9BW]] 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|070R982G4B]]. It is a generalization of the line graph of a [[graph|00C0BR7D7H]].