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Computing the $p$-Spectral Radii of Uniform Hypergraphs with Applications

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Jingya Chang, Weiyang Ding, Liqun Qi, Hong Yan

Combinatorics · Submitted 13 Mar 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

how it is stated · asserted 0.93 read the record →

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arXiv ID1703.04275 (version 1)
Pith IDVZZ3WOMV, Pith's permanent record of this paper and its review
CitationHong Yan, Jingya Chang, Liqun Qi, Weiyang Ding. "Computing the $p$-Spectral Radii of Uniform Hypergraphs with Applications." arXiv:1703.04275 (2017). https://pith.science/paper/VZZ3WOMV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,065 input tokens.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.79 · mentions code or data availability 0.03.

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arXiv listing abstract v1. Results and the main claim are underlined; .

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 stands out among 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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.06 0.04 asserted 1.00
s1 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). method 0.55 0.96 0.27 asserted 1.00
s2 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. result 0.84 0.82 0.19 asserted 0.93
s3 When computing the spectral radius of the adjacency tensor of a uniform hypergraph, CSRH stands out among existing approaches. result 0.66 0.65 0.13 asserted 1.00
s4 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. result 0.68 0.86 0.16 asserted 0.99
s5 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. result 0.55 0.93 0.21 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.75.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original 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 stands out among 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.

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