{
  "aliases": [
    "edge-graph-polytope",
    "edge-graph-of-a-polytope",
    "polytopal-graph",
    "polytope-graph",
    "skeleton-of-a-polytope",
    "vertex-edge-graph-of-a-polytope"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn polytope theory, the **edge graph** (also known as **vertex-edge graph** or just **graph**) of a polytope is a combinatorial graph whose vertices and edges correspond directly to the vertices and edges of the polytope. As a purely [[combinatorial|0JKW7W7XFR]] object, the edge graph encodes incidence information, capturing which vertices are connected by edges, but it does not retain geometric data such as vertex positions or edge lengths. Further common names for the edge graph are **skeleton** and **1-skeleton**, though some authors reserve these terms for the geometric embedding formed by the vertices and edges in the polytope's ambient space. There is no universally agreed upon notation for the edge graph of a polytope $P$. Common notations include $G_P$, $G(P)$ or $\\operatorname{skel}(P)$.\n",
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  "front": {
    "aliases": [
      "edge-graph-polytope",
      "edge-graph-of-a-polytope",
      "polytopal-graph",
      "polytope-graph",
      "skeleton-of-a-polytope",
      "vertex-edge-graph-of-a-polytope"
    ],
    "inventory": [
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    "kind": "concept",
    "name": "Graph of a polytope",
    "same_as": {
      "wikidata": "Q135553266",
      "wikipedia": "Graph of a polytope"
    },
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        "locator": "Graph of a polytope",
        "mention": "wikipedia://en/74718534",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:74718534@r1367982734"
      }
    ],
    "tag": "S6HMSC7N54"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/S6HMSC7N54/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/S6HMSC7N54.md",
  "msc": null,
  "name": "Graph of a polytope",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/S6H/S6HMSC7N54.md",
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  "tag": "S6HMSC7N54",
  "uri": "m2://S6HMSC7N54",
  "url": "https://math2.tamnd.com/wiki/graph-of-a-polytope/",
  "writing": {
    "tag": "S6HMSC7N54",
    "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
      }
    ]
  }
}