Computing the p-Spectral Radii of Uniform Hypergraphs with Applications

Jingya Chang, Weiyang Ding, Liqun Qi*, Hong Yan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

14 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-25
Number of pages25
JournalJournal of Scientific Computing
Volume75
Issue number1
DOIs
Publication statusPublished - 1 Apr 2018

User-Defined Keywords

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

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