复杂网络零模型的构造及应用

Real-life complex networks have various scales and complicated structures, so absolute values of various statistics are often unable to depict the complexity of a network. Based on absolute values of various statistics, the results of quantitative analysis are not accurate enough, and sometimes the results of the qualitative analysis are not exact. The null model of a network refers to the randomized copy that has some of the same properties as the original network, and the appropriate null model is the best reference to the original network. Therefore, null models combined with statistics index can accurately depict non-trivial properties of real complex networks. In this project, we try to from simple to complex build the suitable null networks for signed networks, weighted networks, temporal networks and multilayer networks. Especially, we focus on the construction process and practical application of the null model based on Randomized algorithms. For each type of networks, we try to build a collection of null hypothesis networks, and construct the corresponding multi-scale statistics system. The theoretical value of this project is that the classic hypothesis test is introduced to the emerging field of network science, which can help us to systematically find the nontrivial complexity of real networks, quantify the measures of real networks, and explore the causes of real networks. Finally, we can analyze real network properties to know their quantized impact on the performance of practical applications based on null networks, and then propose some more effective algorithms for practical applications.

实证网络的规模大小各异、结构千差万别，因此各种统计量的绝对数值往往无法刻画网络的复杂特性，不仅定量分析上不够精确，有时甚至连定性分析的结果都不准确。网络的零模型是指与原始网络具有某些相同性质的随机化副本，好的零模型是原始网络的最佳参照物，结合对应的统计量指标可准确刻画出实际网络非平凡特性的来源和程度。本项目由简单到复杂逐步构建符号网络、加权网络、时效网络和双层网络上适用的零模型网络，重点研究基于置乱算法的零模型构造过程和它们的实际应用。针对每种类型网络建立一个层层递进的零假设网络集合，并构建出对应的多尺度统计量体系。本项目的理论价值是将经典的假设检验过程引入到新兴的网络科学领域，可系统性地对实证网络的复杂性进行发现、度量和寻因：发现网络的某种非平凡性质，量化这种性质的程度，对这种性质产生的原因进行探究。最后，基于零模型可精确分析出网络性质如何影响实际应用的性能，具有广泛的实际应用前景。

复杂网络是指由数量巨大的节点在一定时间尺度上相互影响共同构成的复杂系统，在网络科学领域重点关注复杂网络中存在的非平凡性质以及这些性质的生成机理。在实证网络研究中，一般会使用多种统计量来刻画复杂网络的性质。由于各种统计量的绝对数值往往是无量纲的，而且由于不同网络的规模大小各异、结构千差万别，直接分析实证网络的结果在定性和定量上均不够准确，因此本项目中把与实证网络具有某些相同性质的随机化网络称为该网络的零模型网络。本项目中对复杂网络零模型的构造方法和相关应用进行了系统而全面的研究，分析了无权网络、符号网络、加权网络、时效网络和双层网络上各种零模型的构造方法和过程，将经典的假设检验过程引入到新兴的网络科学领域。不但深入分析在各类网络中零模型网络的构造方法，构建了一套从简单到复杂、层层递进的零模型集合，同时也研究了这些零模型网络在符号预测、链路预测、社团检测等多种实际场景中的应用。复杂网络零模型能为实证网络提供一个准确的参照，结合统计量指标可以准确描述实证网络的非平凡特性，有助于揭示复杂网络复杂性的来源和程度。可以分析出实证网络的哪些特性影响了这些应用的效果，从而提出更有效的预测算法或检测模型，具有广泛的实际应用前景。