{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "BBR7QAD87Y"
    },
    {
      "field": "defines",
      "target": "GZKMX0WRA5"
    }
  ],
  "body": "\n## Summary\n\nThe Cheeger constant of a finite graph measures its worst bottleneck.\nIt is the least ratio of the number of edges leaving a set of vertices to the size of the set.\nThe minimum runs over the sets with at most half of the vertices.\nIt is zero exactly for disconnected graphs, and it is large when every set of vertices has many edges to its complement.\nIt is also called the edge expansion or isoperimetric number, and bounded-degree graphs with Cheeger constant bounded below are [[expander graphs|DXJXVFV79H]].\nThe Cheeger inequalities compare it with the second smallest eigenvalue of the [[Laplacian matrix|TN6M6DVZRP]].\n\n## Explanations\n\n### L1 human\n\nTry to cut a graph into two parts so that few edges cross the cut, while the smaller part is still big.\nThe Cheeger constant is the best ratio you can get: crossing edges divided by the size of the smaller part.\nA long path has a tiny Cheeger constant, since one edge cuts it in half.\nA complete graph has a large one, since every cut crosses many edges.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "05C50",
      "05C40",
      "05C48"
    ],
    "name": "Cheeger constant",
    "same_as": {
      "wikidata": "Q5089262",
      "wikipedia": "Cheeger constant (graph theory)"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Cheeger_constant_(graph_theory)"
      }
    ],
    "tag": "Y7S6W12N64"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/Y7S6W12N64/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/Y7S6W12N64.md",
  "msc": [
    "05C50",
    "05C40",
    "05C48"
  ],
  "name": "Cheeger constant",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/Y7S/Y7S6W12N64.md",
  "status": null,
  "tag": "Y7S6W12N64",
  "uri": "m2://Y7S6W12N64",
  "url": "https://math2.tamnd.com/wiki/cheeger-constant/",
  "writing": {
    "tag": "Y7S6W12N64",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}