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通过树计数高效检验网络相关性AI 解读

We propose a new procedure for testing whether two networks are edge-correlated through some latent vertex correspondence. The test statistic is based on counting the cooccurrences of signed trees for a family of nonisomorphic trees. When the two networks are Erdős–Rényi random graphs G(n,q) that are either independent or correlated with correlation coefficient ρ, our test runs in n2+o(1) time and succeeds with high probability as n→∞, provided that nmin{q,1−q}≥n−o(1) and…

度修正随机分块模型的凸化模块度最大化AI 解读

The stochastic block model (SBM), a popular framework for studying community detection in networks, is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of SBM that allows for degree heterogeneity within communities. To find the communities under DCSBM, this paper proposes a convexified modularity maximization approach, which…