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Title: Computing the p-spectral radii of uniform hypergraphs with applications
Authors: Chang, JY 
Ding, WY 
Qi, LQ 
Yan, H
Keywords: Eigenvalue
Large scale tensor
Network analysis
P-spectral radius
Issue Date: 2018
Publisher: Springer
Source: Journal of scientific computing, Apr. 2018, v. 75, no. 1, p. 1-25 How to cite?
Journal: Journal of scientific computing 
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.
ISSN: 0885-7474
DOI: 10.1007/s10915-017-0520-x
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