## Abstract

The p-spectral radius of a uniform hypergraph covers many important concepts, such as Lagrangian and spectral radius of the hypergraph, and is crucial for solving spectral extremal problems of hypergraphs. In this paper, we establish a spherically constrained maximization model and propose a first-order conjugate gradient algorithm to compute the p-spectral radius of a uniform hypergraph (CSRH). By the semialgebraic nature of the adjacency tensor of a uniform hypergraph, CSRH is globally convergent and obtains the global maximizer with a high probability. When computing the spectral radius of the adjacency tensor of a uniform hypergraph, CSRH outperforms existing approaches. Furthermore, CSRH is competent to calculate the p-spectral radius of a hypergraph with millions of vertices and to approximate the Lagrangian of a hypergraph. Finally, we show that the CSRH method is capable of ranking real-world data set based on solutions generated by the p-spectral radius model.

Original language | English |
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Pages (from-to) | 1-25 |

Number of pages | 25 |

Journal | Journal of Scientific Computing |

Volume | 75 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Apr 2018 |

## Scopus Subject Areas

- Software
- Theoretical Computer Science
- Numerical Analysis
- Engineering(all)
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics

## User-Defined Keywords

- Eigenvalue
- Hypergraph
- Large scale tensor
- Network analysis
- p-spectral radius
- Pagerank