{
  "id": "1605.09281",
  "version": "v1",
  "published": "2016-05-30T15:36:31.000Z",
  "updated": "2016-05-30T15:36:31.000Z",
  "title": "On the principal eigenvectors of uniform hypergraphs",
  "authors": [
    "Lele Liu",
    "Liying Kang",
    "Xiying Yuan"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{A}(H)$ be the adjacency tensor of $k$-uniform hypergraph $H$. If $H$ is connected, the unique positive eigenvector $x=(x_1,x_2,\\cdots,x_n)^T$ with $||x||_k=1$ corresponding to spectral radius $\\rho(H)$ is called the principal eigenvector of $H$. In this paper, we investigate the bounds of the maximal entry in the principal eigenvector of $H$. Meanwhile, we also obtain some bounds of the ratio $\\frac{x_i}{x_j}$ for any $i$, $j\\in [n]$. Based on these previous results, we finally give an estimate of the gap of spectral radii between $H$ and proper sub-hypergraph $H'$ of $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-30T15:36:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A42",
      "05C50"
    ],
    "keywords": [
      "principal eigenvector",
      "uniform hypergraph",
      "spectral radius",
      "unique positive eigenvector",
      "adjacency tensor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}