AN Lp THEORY OF SPARSE GRAPH CONVERGENCE I: LIMITS, SPARSE RANDOM GRAPH MODELS, AND POWER LAW DISTRIBUTIONS
AN Lp THEORY OF SPARSE GRAPH CONVERGENCE I: LIMITS, SPARSE RANDOM GRAPH MODELS, AND POWER LAW DISTRIBUTIONS
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DOI：
10.1090/tran/7543
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发表时间：
2019-09-01
影响因子：
1.3
通讯作者：
Zhao, Yufei
中科院分区：
文献类型：
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作者：
Borgs, Christian;Chayes, Jennifer T.;Zhao, Yufei
在L-p图的基础上，提出并发展了稀疏图序列的极限理论，将现有的密集图极限的l -无穷理论及其由Bollobas和Riordan推广到无密集点稀疏图的理论进行了推广。在这样做的过程中，我们用较弱的假设取代了无密集点假设，这使我们能够分析具有幂律度分布的图形。给出了具有无界平均度的稀疏图的第一个广泛适用的极限理论。在本文中，我们奠定了图子的L-p理论的基础，刻画了收敛性，并建立了相应的随机图模型，同时我们在另一篇论文中证明了几个替代度量的等价性。
We introduce and develop a theory of limits for sequences of sparse graphs based on L-p graphons, which generalizes both the existing L-infinity theory of dense graph limits and its extension by Bollobas and Riordan to sparse graphs without dense spots. In doing so, we replace the no dense spots hypothesis with weaker assumptions, which allow us to analyze graphs with power law degree distributions. This gives the first broadly applicable limit theory for sparse graphs with unbounded average degrees. In this paper, we lay the foundations of the L-p theory of graphons, characterize convergence, and develop corresponding random graph models, while we prove the equivalence of several alternative metrics in a companion paper.