复杂网络的自我相似性
Chaoming Song1, Shlomo Havlin, Hernán A Makse
1Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
Nature
|January 28, 2005
概括
复杂的网络在所有尺度上都表现出自我重复的模式,挑战以前的假设. 这一发现揭示了有限的自我相似指数,解释了它们的无尺度性质,并暗示了普遍的自我组织动态.
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:
- 复杂的网络,包括互联网和生物系统,往往没有规模,表现出权力法度分布.
- 现有的理论表明,复杂网络由于其小世界特性,在长度尺度转换下缺乏不变性.
- 这种感知到的缺乏自我相似性与碎形或自我相似结构的预期行为相矛盾.
研究的目的:
- 调查现实世界复杂网络的规模不变性和自我相似性.
- 挑战普遍认为复杂网络在不同长度尺度上不是自我相似的观点.
- 识别控制复杂网络结构和组织的基本属性.
主要方法:
- 对各种现实世界复杂网络的分析.
- 应用重新规范化程序,包括粗粒化到不同尺寸的盒子中.
- 量化盒子数量与盒子大小之间的关系,以确定缩放指数.
主要成果:
- 与先前的信念相反,复杂网络在所有长度尺度上都表现出自我重复的模式.
- 在覆盖网络所需的盒子数量和这些盒子的大小之间确定了权力法关系.
- 对于这些复杂的网络,确定了一个有限的自相似指数.
结论:
- 复杂网络表现出固有的自我相似性,其特点是有限的扩展指数.
- 鉴定到的自我相似性为许多现实世界的网络所观察到的无尺度属性提供了基本的解释.
- 这些发现表明,共同的潜在自我组织机制驱动着复杂网络结构的形成.
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