复杂网络的可压缩性
Compressibility of complex networks
摘要：
许多复杂的网络依赖于生物实体来保存。从人类认知到进化，这些实体必须首先编码，然后在明显的资源限制下复制这些网络。幸存的网络是那些服从约束编码的网络，或者换句话说，是可压缩的。但网络的可压缩性如何呢？什么特征使一个网络比另一个更可压缩？在这里，我们通过将网络建模为信息源来回答这些问题，然后使用率失真理论对其进行压缩。每个网络产生一个唯一的率失真曲线，它指定了在给定的描述尺度下保留的最小信息量。然后，网络的可压缩性出现了一个自然的定义：通过压缩可以去除的信息量，在所有尺度上平均。分析一系列真实和模型网络，我们证明了可压缩性随着两个常见的网络属性而增加：传递性（或聚类）和度异质性。这些结果表明，层次组织-这是由模块化结构和异构度的特点-促进复杂网络中的压缩。一般来说，我们的框架揭示了网络的结构和其被压缩的能力之间的相互作用，使调查压缩在塑造现实世界的网络中的作用。
英文摘要：
Many complex networks depend upon biological entities for their preservation. Such entities, from human cognition to evolution, must first encode and then replicate those networks under marked resource constraints. Networks that survive are those that are amenable to constrained encoding, or, in other words, are compressible. But how compressible is a network? And what features make one network more compressible than another? Here we answer these questions by modeling networks as information sources before compressing them using rate-distortion theory. Each network yields a unique rate-distortion curve, which specifies the minimal amount of information that remains at a given scale of description. A natural definition then emerges for the compressibility of a network: the amount of information that can be removed via compression, averaged across all scales. Analyzing an array of real and model networks, we demonstrate that compressibility increases with two common network properties: transitivity (or clustering) and degree heterogeneity. These results indicate that hierarchical organization -- which is characterized by modular structure and heterogeneous degrees -- facilitates compression in complex networks. Generally, our framework sheds light on the interplay between a network's structure and its capacity to be compressed, enabling investigations into the role of compression in shaping real-world networks.
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。
