在加权模块化网络中的可检测性值
Filippo Radicchi1, Filipi N Silva1, Alessandro Flammini1
1Indiana University, Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Bloomington, Indiana 47408, USA.
Physical review. E
|February 20, 2026
概括
在网络中检测社区结构是可能的,直到一定混合值. 这个值取决于节点度和边缘重量分布,重量的更高变化阻碍检测.
科学领域:
- 网络科学 网络科学
- 统计物理学的统计物理.
- 数据分析数据分析
背景情况:
- 社区检测算法旨在识别网络中的节点组.
- 权重植区分区模型是评估社区检测方法的标准基准.
- 光谱模块化优化是社区检测的一个常见技术.
研究的目的:
- 确定在加权网络中检测基准真相分区所必需的条件.
- 通过分析推导出光谱模块化优化所能承受的最大混合水平.
- 调查不同边缘重量分布对社区检测能力的影响.
主要方法:
- 可检测性值的分析推导.
- 对两个大小相同的社区的加权种植分区模型的分析.
- 在Poisson分布的节点度下比较五个边缘重量分布 (Dirac,Poisson,指数,几何,签名Bernoulli)
主要成果:
- 可检测性值取决于节点度和边缘重量分布的前两个时刻.
- 迪拉克分布式权重导致最小的检测值.
- 以指数分布的重量将值增加一个sqrt的因子[2];更高的重量变化可能会降低检测能力.
结论:
- 边缘重量变化显著影响社区结构的可检测性.
- 结合边缘权重是有害的,当它们不携带有关社区结构的信息.
- 这些发现提供了关于加权网络中光谱模块化优化的局限性和性能的见解.
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