标记网络的基本统计特征和自相似性质
Fundamental statistical features and self-similar properties of tagged networks
摘要：
我们调查的基本统计特征的标记（或注释）网络具有丰富的各种属性与它们的节点。标签（属性、注释、特性、功能等）提供关于由给定节点表示的实体的基本信息，因此，考虑它们是朝着更完整地描述大型复杂系统的结构迈出的重要一步。我们的主要目标是揭示节点标签的统计属性与图拓扑的统计属性之间的关系。为了更好地识别带有标记节点的网络，我们引入了一些新的概念，包括标记性（将链接概率与节点相似性联系起来），以及新的数量，如节点唯一性（衡量节点的标记在网络中出现的概率）和标记性指数。我们将我们的方法应用于三个大型网络，代表复杂系统的不同领域。多个标签相关量显示类似的行为（例如，我们所研究的网络是标记性的，指示标记相对于拓扑的可能的通用方面），而一些其它特征（例如节点唯一性的分布）显示出网络之间的可变性，从而允许精确定位真实世界复杂网络的大规模特定特征。我们还发现，对于每个网络的拓扑结构和标签的分布是规模不变的，这种自相似的网络属性可以很好地表征的标签的可伸缩性指数，这是特定于每个系统。
英文摘要：
We investigate the fundamental statistical features of tagged (or annotated) networks having a rich variety of attributes associated with their nodes. Tags (attributes, annotations, properties, features, etc.) provide essential information about the entity represented by a given node, thus, taking them into account represents a significant step towards a more complete description of the structure of large complex systems. Our main goal here is to uncover the relations between the statistical properties of the node tags and those of the graph topology. In order to better characterise the networks with tagged nodes, we introduce a number of new notions, including tag-assortativity (relating link probability to node similarity), and new quantities, such as node uniqueness (measuring how rarely the tags of a node occur in the network) and tag-assortativity exponent. We apply our approach to three large networks representing very different domains of complex systems. A number of the tag related quantities display analogous behaviour (e.g., the networks we studied are tag-assortative, indicating possible universal aspects of tags versus topology), while some other features, such as the distribution of the node uniqueness, show variability from network to network allowing for pin-pointing large scale specific features of real-world complex networks. We also find that for each network the topology and the tag distribution are scale invariant, and this self-similar property of the networks can be well characterised by the tag-assortativity exponent, which is specific to each system.
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。
