网络在复杂性-熵平面上的映射与判别
Mapping and discrimination of networks in the complexity-entropy plane
摘要：
复杂网络通常以其拓扑、空间或信息理论属性来表征，并且相关度量的组合用于将网络区分为不同的类别或类别。然而，即使有目前的各种特性，它仍然是当前研究的主题，以适当地量化网络的复杂性，并相应地区分不同类型的复杂网络，如基础设施或社交网络，在此基础上。在这里，我们探讨了通过统计复杂性度量对复杂网络进行分类的可能性，该度量以前已成功地应用于区分不同类型的混沌和随机时间序列。它是由网络的平均每个节点的熵测量表征网络的信息内容和相关的詹森-香农分歧作为衡量不平衡。我们研究了29个真实世界的网络，并表明同一类别的网络往往聚集在所产生的复杂性熵平面的不同区域。我们证明，在我们的框架内，连接体网络表现出最高的复杂性，而例如，交通和基础设施网络显示显着较低的价值。此外，我们通过将其应用于随机无标度网络和Watts-Strogatz模型网络来证明我们的框架的实用性。然后，我们在第二个应用中表明，通过选择阈值以使统计网络复杂性最大化，所提出的框架对于客观构建基于阈值的网络（例如功能性气候网络或递归网络）是有用的。
英文摘要：
Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here, we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged per-node entropic measure characterizing the network's information content and the associated Jenson-Shannon divergence as a measure of disequilibrium. We study 29 real world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g, transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.
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