AI 中文总结
本研究测量近一百个真实网络，发现社区数量随规模呈指数介于1/2和2/3之间的幂律增长，并指出局部增长规则可解释该超分形指数。
AI 中文摘要
大多数网络，从友谊网络到互联网，都会分解为社区：即节点组，组内节点之间的连接比与组外节点的连接更紧密。一个基本问题仍然悬而未决：一个网络应该有多少个社区，以及这个数量如何随规模增长？简单模型界定了可能性范围。在由密集模块构建的小世界网络——即团构成的穴居人图——中，每个模块就是一个社区，因此社区数量随规模成比例增长，即$n$。在自相似的分形网络中，社区数量增长要慢得多，与平方根成正比。真实网络可能位于两者之间的任何位置。在这里，我们测量了近一百个真实网络中的社区数量，这些网络跨越四个数量级，从拥有34个成员的俱乐部到拥有数百万个节点的网络，并且在单个系统中随着其增长进行了数十年的追踪。我们发现了一个指数介于二分之一和三分之二之间的幂律——高于分形值，低于线性极限。通过局部规则进行网络增长的简单模型再现了相同的超分形指数，这是网络组织的一个稳定且可测量的属性。简而言之，网络演化将系统的组成部分聚集成簇，其数量随规模呈幂律增长。
英文摘要
Most networks, from friendships to the internet, break up into communities: groups of nodes more densely connected to one another than to the rest. A basic question has remained open: how many communities should a network have, and how does that number grow with size? Simple models bracket the possibilities. In a small-world network built from dense modules -- a caveman graph of cliques -- each module is a community, so the number grows in proportion to size, as $n$. In self-similar, fractal networks it grows far more slowly, as the square root. Real networks could lie anywhere between. Here we measure the number of communities across close to a hundred real networks spanning four orders of magnitude, from a $34$-member club to millions of nodes, and within individual systems followed over decades as they grow. We find a power law with an exponent between one half and two thirds -- above the fractal value and below the linear limit. Simple models of network growth by local rules reproduce the same super-fractal exponent, a stable and measurable property of network organization. In short, network evolution herds a system's components into clusters, whose number grows as a power law of size.
Comments6 pages, 4 figures
