Quantifying the compressibility of complex networks.
Quantifying the compressibility of complex networks.
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量化复杂网络的可压缩性。
DOI：
10.1073/pnas.2023473118
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发表时间：
2021-08-10
影响因子：
11.1
通讯作者：
Bassett DS
中科院分区：
文献类型：
--
作者：
Lynn CW;Bassett DS
现实世界的网络是复杂的，由大量相互连接的元素组成，执行各种各样的社会和生物功能。然而，在许多网络中，共同的是被有效压缩的压力，无论是在大脑中还是在遗传密码中。但是，正如计算机上的文件可以被压缩到不同的程度，是什么让一个网络比另一个更可压缩？为了回答这个问题，我们采用信息论的工具来量化网络的可压缩性。研究现实世界和模型网络，我们发现，层次组织紧密的集群和异构度增加压缩性，使压缩表示跨尺度。一般来说，我们的框架提供了一个信息理论的方法来研究网络结构和压缩之间的相互作用。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。幸存下来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。通过分析一系列真实的和模型网络，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，层次组织的特点是模块化的结构和异构度，有利于复杂网络中的压缩。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。
Real-world networks are complex, comprising vast webs of interconnected elements performing a diverse array of social and biological functions. Common among many networks, however, is the pressure to be efficiently compressed—either in the brain or in the genetic code. But just as files on a computer can be compressed to differing degrees, what makes one network more compressible than another? To answer this question, we adapt tools from information theory to quantify the compressibility of a network. Studying real-world and model networks, we find that hierarchical organization—with tight clustering and heterogeneous degrees—increases compressibility, enabling compressed representations across scales. Generally, our framework provides an information-theoretic method for investigating the interplay between network structure and compression. 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.
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DOI：
10.1523/jneurosci.1929-08.2008
发表时间：
2008-09-10
期刊：
The Journal of neuroscience : the official journal of the Society for Neuroscience
影响因子：
--
作者：
Bassett DS;Bullmore E;Verchinski BA;Mattay VS;Weinberger DR;Meyer-Lindenberg A
通讯作者：
Meyer-Lindenberg A
影响因子：
2.4
作者：
Kalakoski, V;Saariluoma, P
通讯作者：
Saariluoma, P
影响因子：
4.3
作者：
Friston K
通讯作者：
Friston K
影响因子：
--
作者：
Leskovec, Jure;Lang, Kevin J.;Mahoney, Michael W.
通讯作者：
Mahoney, Michael W.
影响因子：
25
作者：
Dworkin, Jordan D.;Linn, Kristin A.;Bassett, Danielle S.
通讯作者：
Bassett, Danielle S.