{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "0VSNHTHK8T"
    },
    {
      "field": "uses",
      "target": "0XAP8WHNES"
    }
  ],
  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] with vertex set $V$ and adjacency relation $\\sim$.\nThe edge set of $G$ is the set\n$$E(G) = \\{ \\{u, v\\} : u, v \\in V,\\ u \\sim v \\}$$\nof unordered pairs of adjacent vertices.\n\n## Remarks\n\nEach edge is a $2$-element subset of $V$, because $\\sim$ is irreflexive.\nThe number of edges $|E(G)|$ is the size of $G$, and the number of vertices $|V|$ is its order.\nThe [[handshaking lemma|0XAP8WHNES]] relates $|E(G)|$ to the degrees of the vertices.\n\n## Explanations\n\n### L1 human\n\nThe edge set is the list of all lines of the graph, with each line given by its two end points.\nA triangle on the vertices $a, b, c$ has the edge set $\\{\\{a, b\\}, \\{b, c\\}, \\{a, c\\}\\}$.\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "defines": "0AQBSVMX9P",
    "kind": "definition",
    "msc": [
      "05C99"
    ],
    "name": "Edge set",
    "sources": [
      {
        "locator": "E",
        "url": "https://en.wikipedia.org/wiki/Glossary_of_graph_theory"
      }
    ],
    "tag": "0WNGQBPPQX",
    "uses": [
      "0JD5C82QMB"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/0WNGQBPPQX/",
  "links": [
    {
      "field": "defines",
      "target": "0AQBSVMX9P"
    },
    {
      "field": "uses",
      "target": "0JD5C82QMB"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0WNGQBPPQX.md",
  "msc": [
    "05C99"
  ],
  "name": "Edge set",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0WN/0WNGQBPPQX.md",
  "status": null,
  "tag": "0WNGQBPPQX",
  "uri": "m2://0WNGQBPPQX",
  "url": "https://math2.tamnd.com/wiki/edge-set-definition/",
  "writing": {
    "tag": "0WNGQBPPQX",
    "kind": "definition",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}