{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nTwo vertices $u,v$ are true twins if they have the same closed neighborhood: $N_{G}[u] = N_{G}[v]$ (this implies $u$ and $v$ are neighbors), and they are false twins if they have the same open neighborhood: $N_{G}(u) = N_{G}(v))$ (this implies $u$ and $v$ are not neighbors).\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "Y051NHCDS4"
    ],
    "kind": "concept",
    "name": "Twin",
    "sources": [
      {
        "locator": "Glossary of graph theory, section T",
        "mention": "wikipedia://en/325802#DGPI",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:325802@r1373839425"
      }
    ],
    "tag": "6NCN51F7AE"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/6NCN51F7AE/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/6NCN51F7AE.md",
  "msc": null,
  "name": "Twin",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/6NC/6NCN51F7AE.md",
  "status": null,
  "tag": "6NCN51F7AE",
  "uri": "m2://6NCN51F7AE",
  "url": "https://math2.tamnd.com/wiki/twin/",
  "writing": {
    "tag": "6NCN51F7AE",
    "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
      }
    ]
  }
}