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arXiv 2604.18565cs.SI
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网络中少数群体社区的可检测性

Detectability of minority communities in networks

Maastricht University(马斯特里赫特大学)

Jiaze Li, Leto Peel

AI总结:

研究从理论角度探讨网络中少数群体社区的可检测性,通过随机块模型识别三个阶段:可检测、可区分和可解决,揭示了谱聚类在细粒度社区结构识别上的局限性。

摘要:

社区结构在现实网络中普遍存在,实证研究揭示了异质分布,其中少数主导多数社区与许多小群体共存。这些小规模群体,我们称之为少数群体社区,对理解网络组织至关重要,但检测具有挑战性。本文从理论角度利用随机块模型研究少数群体社区的可检测性,识别三个阶段:可检测阶段中整体社区结构可恢复但少数群体被合并到多数群体中;可区分阶段中少数群体形成一个与多数群体分离的群体但内部未解决;可解决阶段中每个少数群体完全可区分。这些阶段对应Kesten-Stigum阈值和信号矩阵特征值结构决定的两个额外阈值。此外,研究显示谱聚类在少数群体社区检测上的表现弱于信念传播,揭示了谱方法在识别细粒度社区结构上的局限性,尽管其能检测到理论极限下的宏观结构。

英文摘要:

Community structure is prevalent in real-world networks, with empirical studies revealing heterogeneous distributions where a few dominant majority communities coexist with many smaller groups. These small-scale groups, which we term minority communities, are critical for understanding network organization but pose significant challenges for detection. Here, we investigate the detectability of minority communities from a theoretical perspective using the Stochastic Block Model. We identify three distinct phases of community detection: the detectable phase, where overall community structure is recoverable but minority communities are merged into majority groups; the distinguishable phase, where minority communities form a coherent group separate from the majority but remain unresolved internally; and the resolvable phase, where each minority community is fully distinguishable. These phases correspond to phase transitions at the Kesten-Stigum threshold and two additional thresholds determined by the eigenvalue structure of the signal matrix, which we derive explicitly. Furthermore, we demonstrate that spectral clustering with the Bethe Hessian exhibits significantly weaker detection performance for minority communities compared to belief propagation, revealing a specific limitation of spectral methods in identifying fine-grained community structure despite their capability to detect macroscopic structures down to the theoretical limit.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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