Abstract
Non-backtracking PageRank is a variation of Google’s PageRank, which is based on non-backtracking random walk. However, if the number of dangling nodes of a graph is large, the non-backtracking PageRank algorithm proposed in [F. Arrigo, D. Higham, and V. Noferini, Non-backtracking PageRank, Journal of Scientific Computing, 80: 1419–1437, 2019] may suffer from huge memory requirements and heavy computational costs. Thus, the non-backtracking PageRank algorithm is only applicable to small-scale or medium-sized graphs with few dangling nodes. In this work, we first consider how to compute the non-backtracking PageRank vector efficiently by using the Jacobi iteration, and then propose two strategies to speed up the computation of non-backtracking PageRank, in which we add some edges to a graph in a randomized and a fixed way, respectively. The computational issues are discussed in detail. The advantages of the proposed algorithms are two-fold. First, the sizes of the matrix computation problems are much smaller than that of the original one. Second, there is no kronecker product in the involved non-backtracking edge matrices, and the structures of the non-backtracking PageRank problems are greatly simplified. Comprehensive numerical experiments are performed on some real-world network matrices, which show that the solutions obtained from the two proposed algorithms and that from the original non-backtracking PageRank algorithm are highly correlated, while the two proposed algorithms can be tens or even hundreds times faster than their original counterpart.
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Acknowledgements
We would like to express our sincere thanks to the anonymous referees and our editor for insightful comments and suggestions that greatly improved the quality of this paper. Meanwhile, we thank Dr. Yongyan Guo and Miss Qing Yu for helpful discussions on an early version of this paper.
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This work is supported by the National Natural Science Foundation of China under Grant 12271518, the Fujian Natural Science Foundation under Grant 2023J01354, the Key Research and Development Project of Xuzhou Natural Science Foundation under Grant KC22288, and the Open Project of Key Laboratory of Data Science and Intelligence Education of the Ministry of Education under Grant DSIE202203.
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Zhang, Y., Wu, G. Two Accelerated Non-backtracking PageRank Algorithms for Large-scale Networks. J Sci Comput 102, 3 (2025). https://doi.org/10.1007/s10915-024-02735-7
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DOI: https://doi.org/10.1007/s10915-024-02735-7