Faculty of Engineering, University of Porto, Porto, Portugal.
Department of Industrial and Systems Engineering, Rensselaer Polytechnic Institute, Troy , NY, United States of America.
PLoS One. 2020 Aug 12;15(8):e0236753. doi: 10.1371/journal.pone.0236753. eCollection 2020.
Dynamical networks are pervasive in a multitude of natural and human-made systems. Often, we seek to guarantee that their state is steered to the desired goal within a specified number of time steps. Different network topologies lead to implicit trade-offs between the minimum number of driven nodes and the time-to-control. In this study, we propose a generative model to create artificial dynamical networks with trade-offs similar to those of real networks. Remarkably, we show that several centrality and non-centrality measures are not necessary nor sufficient to explain the trade-offs, and as a consequence, commonly used generative models do not suffice to capture the dynamical properties under study. Therefore, we introduce the notion of time-to-control communities, that combine networks' partitions and degree distributions, which is crucial for the proposed generative model. We believe that the proposed methodology is crucial when invoking generative models to investigate dynamical network properties across science and engineering applications. Lastly, we provide evidence that the proposed generative model can generate a variety of networks with statistically indiscernible trade-offs (i.e., the minimum number of driven nodes vs. the time-to-control) from those steaming from real networks (e.g., neural and social networks).
动力网络在众多自然和人为系统中普遍存在。通常，我们试图保证它们的状态在规定的时间内被引导到期望的目标。不同的网络拓扑结构导致了驱动节点的最小数量和控制时间之间的隐性权衡。在这项研究中，我们提出了一种生成模型，用于创建具有与真实网络相似权衡的人工动力网络。值得注意的是，我们表明，几个中心性和非中心性度量既不是必要的，也不是充分的，无法解释这些权衡，因此，常用的生成模型不足以捕捉所研究的动力性质。因此，我们引入了控制时间社区的概念，它结合了网络的分区和度分布，这对所提出的生成模型至关重要。我们相信，当在科学和工程应用中调用生成模型来研究动力网络性质时，所提出的方法是至关重要的。最后，我们提供了证据表明，所提出的生成模型可以从真实网络（例如，神经网络和社交网络）生成各种具有统计上不可区分的权衡（即，驱动节点的最小数量与控制时间）的网络。
