加权网络的常用统计量

加权网络是复杂网络研究的一个重要分支,连边权重的异质性有助于刻画复杂系统的各种特性.但长期以来,由于加权网络上各种统计量的定义不统一、物理意义不明确,很多学者直接抛弃交互作用的强度,使用门限值将加权网络变为二值无权网络后再进行研究.本文综述了加权网络上常用的统计量,并简要介绍了这些统计量在实际复杂系统分析中的应用.本研究有助于相关研究人员明确各种加权网络统计量的物理意义,使用加权网络对复杂系统进行分析和刻画.同时,理解各种常用统计量的内在联系和应用背景是构造更有效加权网络统计量的基础.最后介绍了各种权重网络的随机化置乱方法,为分析和理解实际加权网络统计量的绝对值提供了参考和比较.

Fundamental Statistics of Weighted Networks

At the present time,all kinds of statistics of weighted networks have not a unified definition and their physical significances are not very clear.Therefore,many researchers turn to discard link weights using the threshold method and study the unweighted version of complex systems. In the paper,fundamental statistics of weighted networks were reviewed and their applications in real-life complex systems were introduced.The study is helpful to clarify the definition of fundamental statistics of weighted networks,which can be used to analyze and characterize complex systems.Especially,understanding the intrinsic relationships and application backgrounds of these fundamental statistics is the foundation for developing more effective statistics of weighted networks. Several shuffling methods for weighted networks were presented,giving reference and comparison to study a real-life weighted complex network.