{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "M9XF82GGW8"
    },
    {
      "field": "uses",
      "target": "R43K0GTTDS"
    },
    {
      "field": "defines",
      "target": "YNFT400EV9"
    }
  ],
  "body": "\n## Summary\n\nThe incidence matrix of a graph records which vertices lie on which edges.\nIt has a row for each vertex, a column for each edge, and a nonzero entry where the vertex is an end of the edge.\nIn the oriented version the two ends get opposite signs, and the product of the matrix with its transpose is the [[Laplacian matrix|TN6M6DVZRP]].\nMore generally, an incidence matrix describes any incidence relation between two finite sets, such as points and blocks of a design.\n\n## Explanations\n\n### L1 human\n\nMake a table with the vertices of a graph down the side and the edges across the top.\nPut a $1$ in a cell when the vertex is an end of the edge, and $0$ otherwise.\nEach column then has exactly two $1$s, one for each end of the edge, and the row of a vertex has as many $1$s as the vertex has edges.\nThis table is the incidence matrix.\n",
  "commit": "5fc425f97f1f6b11da5892c2948ef8c5d8805665",
  "front": {
    "kind": "concept",
    "msc": [
      "05C50"
    ],
    "name": "Incidence matrix",
    "same_as": {
      "wikidata": "Q939272",
      "wikipedia": "Incidence matrix"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Incidence_matrix"
      }
    ],
    "tag": "9DNFN8M83X"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/9DNFN8M83X/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/9DNFN8M83X.md",
  "msc": [
    "05C50"
  ],
  "name": "Incidence matrix",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/9DN/9DNFN8M83X.md",
  "status": null,
  "tag": "9DNFN8M83X",
  "uri": "m2://9DNFN8M83X",
  "url": "https://math2.tamnd.com/wiki/incidence-matrix/",
  "writing": {
    "tag": "9DNFN8M83X",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}