Computing the $p$-Spectral Radii of Uniform Hypergraphs with Applications
Abstract
The -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 -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 stands out among existing approaches. Furthermore, CSRH is competent to calculate the -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 -spectral radius model.
Keywords
Cite
@article{arxiv.1703.04275,
title = {Computing the $p$-Spectral Radii of Uniform Hypergraphs with Applications},
author = {Jingya Chang and Weiyang Ding and Liqun Qi and Hong Yan},
journal= {arXiv preprint arXiv:1703.04275},
year = {2017}
}