"Laplacian matrix" meaning in All languages combined

{
  "etymology_text": "Named after Pierre-Simon, marquis de Laplace (1749 – 1827), a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.",
  "forms": [
    {
      "form": "Laplacian matrices",
      "tags": [
        "plural"
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      "expansion": "Laplacian matrix (plural Laplacian matrices)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A square n×n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices."
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      "id": "en-Laplacian_matrix-en-noun-u8Kh8Cj3",
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      "raw_glosses": [
        "(graph theory) A square n×n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices."
      ],
      "topics": [
        "graph-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Laplacian matrix",
        "Pierre-Simon Laplace"
      ]
    }
  ],
  "word": "Laplacian matrix"
}

{
  "etymology_text": "Named after Pierre-Simon, marquis de Laplace (1749 – 1827), a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.",
  "forms": [
    {
      "form": "Laplacian matrices",
      "tags": [
        "plural"
      ]
    }
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  "head_templates": [
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  "lang_code": "en",
  "pos": "noun",
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        "en:Graph theory"
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      "glosses": [
        "A square n×n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices."
      ],
      "links": [
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          "graph theory",
          "graph theory"
        ],
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          "degree"
        ]
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      "raw_glosses": [
        "(graph theory) A square n×n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices."
      ],
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        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Laplacian matrix",
        "Pierre-Simon Laplace"
      ]
    }
  ],
  "word": "Laplacian matrix"
}