@article{f44efdc3aa4044138007647d6f251bc2, title = "Computing the p-Spectral Radii of Uniform Hypergraphs with Applications", 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.", keywords = "Eigenvalue, Hypergraph, Large scale tensor, Network analysis, p-spectral radius, Pagerank", author = "Jingya Chang and Weiyang Ding and Liqun Qi and Hong Yan", year = "2018", month = apr, doi = "10.1007/s10915-017-0520-x", language = "English", volume = "75", pages = "1--25", journal = "Journal of Scientific Computing", issn = "0885-7474", publisher = "SPRINGER/PLENUM PUBLISHERS", number = "1", }