Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies and dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged as a general and versatile toolbox for studying such systems. Defined as random networks with given features constrained to match those of an input (empirical) network, they may, for example, be used to identify important features of empirical networks and their effects on dynamical processes unfolding in the network. RRMs are typically implemented as procedures that reshuffle an empirical network, making them very generally applicable. However, the effects of most shuffling procedures on network features remain poorly understood, rendering their use nontrivial and susceptible to misinterpretation. Here we propose a unified framework for classifying and understanding microcanonical RRMs (MRRMs) that sample networks with uniform probability. Focusing on temporal networks, we survey applications of MRRMs found in the literature, and we use this framework to build a taxonomy of MRRMs that proposes a canonical naming convention, classifies them, and deduces their effects on a range of important network features. We furthermore show that certain classes of MRRMs may be applied in sequential composition to generate new MRRMs from the existing ones surveyed in this article. We finally provide a tutorial showing how to apply a series of MRRMs to analyze how different network features affect a dynamic process in an empirical temporal network.
翻译:许多动态系统可以通过作为网络来成功地分析它们。在这些情况下所测量到的网络和动态进程通常表现出多样性、非马尔科维亚的网络和动态特征。这使得它们的分析特别具有挑战性。随机参照模型(RRMS)已成为研究这些系统的一般和多功能工具箱。我们在这里提出了一个统一的网络框架,用于分类和理解与输入(经验)网络(MRMMs)相匹配的样本网络(MRRMs)的特征,例如,它们可以用来确定经验网络的重要特征及其对网络中出现的动态进程的影响。RRMMs通常作为程序来实施,重新整合一个经验网络,使其非常普遍适用。然而,大多数打乱程序对网络特征的影响仍然不甚为人理解,使得其使用不易被误解。我们在这里提出了一个统一的框架,用于分类和理解与输入输入(经验)网络的特征(MRMMRM)网络(MRRMs)的特征,我们以时间网络的系列为重点,我们调查在文献中发现的MRRMRM的系列应用情况,我们利用这个框架来构建一个对MRMRMRM的动态网络进行分类的分类,我们最终在排序中可以展示其某些的分类中产生重要的结果。我们可以进一步展示它们。