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Algorithmic Complexity of Multiplex Networks
Physical Review X ( IF 12.5 ) Pub Date : 2020-06-26 , DOI: 10.1103/physrevx.10.021069 Andrea Santoro , Vincenzo Nicosia
Physical Review X ( IF 12.5 ) Pub Date : 2020-06-26 , DOI: 10.1103/physrevx.10.021069 Andrea Santoro , Vincenzo Nicosia
Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modeling transportation networks, social circles, and the human brain. A fundamental and still open problem is to assess if and when the multilayer representation of a system provides a qualitatively better model than the classical single-layer aggregated network. Here we tackle this problem from an algorithmic information theory perspective. We propose an intuitive way to encode a multilayer network into a bit string, and we define the complexity of a multilayer network as the ratio of the Kolmogorov complexity of the bit strings associated to the multilayer and to the corresponding aggregated graph. We find that there exists a maximum amount of additional information that a multilayer model can encode with respect to the equivalent single-layer graph. We show how our complexity measure can be used to obtain low-dimensional representations of multidimensional systems, to cluster multilayer networks into a small set of meaningful superfamilies, and to detect tipping points in the evolution of different time-varying multilayer graphs. Interestingly, the low-dimensional multiplex networks obtained with the proposed method also retain most of the dynamical properties of the original systems, as demonstrated for instance by the preservation of the epidemic threshold in the multiplex susceptible-infected-susceptible model. These results suggest that information-theoretic approaches can be effectively employed for a more systematic analysis of static and time-varying multidimensional complex systems.
中文翻译:
多重网络的算法复杂度
多层网络保留有关复杂系统各组成部分之间不同交互的完整信息,并且最近证明对建模交通网络,社交圈和人脑非常有用。一个基本且仍未解决的问题是评估系统的多层表示是否以及何时提供比传统的单层聚合网络更好的定性模型。在这里,我们从算法信息论的角度解决这个问题。我们提出了一种将多层网络编码为位串的直观方法,并且将多层网络的复杂度定义为与多层以及相应的聚合图相关联的位串的Kolmogorov复杂度之比。我们发现,对于等效的单层图,多层模型可以编码的附加信息数量最大。我们展示了如何使用复杂性度量来获得多维系统的低维表示,如何将多层网络聚类为一小组有意义的超族,以及如何检测不同时变多层图的演化中的临界点。有趣的是,通过所提出的方法获得的低维多路复用网络也保留了原始系统的大多数动力学特性,例如通过在多路复用易感性感染易感性模型中保留流行阈值来证明。
更新日期:2020-06-26
中文翻译:
多重网络的算法复杂度
多层网络保留有关复杂系统各组成部分之间不同交互的完整信息,并且最近证明对建模交通网络,社交圈和人脑非常有用。一个基本且仍未解决的问题是评估系统的多层表示是否以及何时提供比传统的单层聚合网络更好的定性模型。在这里,我们从算法信息论的角度解决这个问题。我们提出了一种将多层网络编码为位串的直观方法,并且将多层网络的复杂度定义为与多层以及相应的聚合图相关联的位串的Kolmogorov复杂度之比。我们发现,对于等效的单层图,多层模型可以编码的附加信息数量最大。我们展示了如何使用复杂性度量来获得多维系统的低维表示,如何将多层网络聚类为一小组有意义的超族,以及如何检测不同时变多层图的演化中的临界点。有趣的是,通过所提出的方法获得的低维多路复用网络也保留了原始系统的大多数动力学特性,例如通过在多路复用易感性感染易感性模型中保留流行阈值来证明。