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Graphons of Line Graphs 论文更新

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2026年10月9日,arXiv 统计学机器学习栏目发布关于线图的 Graphon 估计方法的论文。论文提出一种通过将稀疏有限图映射到其线图来估计图极限(graphon)的方法。满足“平方度性质”的稀疏图(如星图)会产生稠密线图,从而可借助稠密图极限理论推导收敛,并能在经验上区分不同数量的星图,而原图因稀疏性都收敛到零 graphon。此外,超线性优先连接图几乎必然产生稠密线图,而 Erdos-Renyi 等稠密图的线图则变稀疏并收敛到零 graphon。

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Oct 9, 2026
  1. arXiv · Statistics Machine Learning
    线图的 Graphon 估计方法

    论文提出一种通过将稀疏有限图映射到其线图来估计图极限(graphon)的方法。满足“平方度性质”的稀疏图(如星图)会产生稠密线图,从而可借助稠密图极限理论推导收敛,并能在经验上区分不同数量的星图,而原图因稀疏性都收敛到零 graphon;超线性优先连接图几乎必然产生稠密线图,而 Erdos-Renyi 等稠密图的线图则变稀疏并收敛到零 graphon。

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