{
  "aliases": [
    "intersection-line-graphs-of-hypergraphs",
    "line-graphs-of-hypergraphs",
    "linear-hypergraphs"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn 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]].\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "aliases": [
      "intersection-line-graphs-of-hypergraphs",
      "line-graphs-of-hypergraphs",
      "linear-hypergraphs"
    ],
    "inventory": [
      "C46XQT5VWM"
    ],
    "kind": "concept",
    "name": "Line graph of a hypergraph",
    "same_as": {
      "wikidata": "Q6553253",
      "wikipedia": "Line graph of a hypergraph"
    },
    "sources": [
      {
        "locator": "Line graph of a hypergraph",
        "mention": "wikipedia://en/16181442",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:16181442@r1352725289"
      }
    ],
    "tag": "Z9A4ZHMF4G"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/Z9A4ZHMF4G/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/Z9A4ZHMF4G.md",
  "msc": null,
  "name": "Line graph of a hypergraph",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/Z9A/Z9A4ZHMF4G.md",
  "status": null,
  "tag": "Z9A4ZHMF4G",
  "uri": "m2://Z9A4ZHMF4G",
  "url": "https://math2.tamnd.com/wiki/line-graph-of-a-hypergraph/",
  "writing": {
    "tag": "Z9A4ZHMF4G",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}