偏好节点删除对通过偏好附件演变的网络结构的影响
Barak Budnick1, Ofer Biham1, Eytan Katzav1
1The Hebrew University, Racah Institute of Physics, Jerusalem 9190401, Israel.
Physical review. E
|August 1, 2025
概括
优选节点删除对不断发展的网络产生重大影响,导致从无尺度分布到指数级分布的阶段过渡. 这突出了网络对有针对性的删除的敏感性,与随机删除不同.
科学领域:
- 网络科学 网络科学
- 统计物理 统计物理
- 复杂的系统复杂的系统.
背景情况:
- 了解复杂网络的演变对于各种应用至关重要.
- 偏好的附件模型解释了网络增长,但往往忽略了节点删除效应.
- 与随机删除相比,偏好节点删除对网络结构的影响仍未得到充分研究.
研究的目的:
- 分析在不断发展的网络中偏好节点删除的结构后果.
- 在网络拓上研究优先附加和优先删除之间的相互作用.
- 为了确定网络度分布在哪些条件下表现出无尺度或指数行为.
主要方法:
- 开发一种优先附加-优先删除模型.
- 利用主方程和生成函数形式来研究网络动态.
- 对时间依赖度分布 P_t(k) 和其与静态分布 P_st(k) 的收进行分析.
主要成果:
- 确定了一个关键的增长/收缩率, η_c(m),将不同的网络演变模式分开.
- 在临界速率 (η > η_c(m) 以上,度分布趋于静止形式.
- 一个相位过渡发生在 η=1:对于 η_c(m) < η < 1,分布显示了一个指数尾巴,而在 η=1 (纯增长),它仍然是无尺度的 (权力规律尾巴).
结论:
- 不断发展的网络对偏好的节点删除非常敏感,导致不同的结构性质.
- 优选节点删除可以诱导从无尺度到指数级度分布的过渡,与随机删除不同.
- 这些发现提供了对短暂网络的见解,例如具有高用户周转率的社交平台.
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