评“复杂网络中的动力学与方向性”

Unique superdiffusion induced by directionality in multiplex networks

The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirect…

Digraphs are different: Why directionality matters in complex systems

Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect stability, percolation and other dynamical features. I show here that these topological properties have a common origin, in that the edges of directed networks can be aligned - or not - with a global direction. And I illustrate how this can lead to rich and unexpected dynamical behaviour even in the simplest of models.

Edge directionality properties in complex spherical networks

Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks wh…

影响与可影响性：有向复杂网络中的全局方向性

Influence and Influenceability: Global Directionality in Directed Complex Networks

本文使用Trophic Analysis方法研究有向复杂网络，发现节点影响力和网络可影响性取决于层级结构和全局方向性，为特征向量中心性、动力学行为及博弈策略提供了新解释。

利用方向性增强复杂网络中的同步

Enhancing synchronization by directionality in complex networks

我们提出了一种称为剩余边缘介数梯度（REBG）的方法，通过分配链路方向，同时保持网络拓扑结构和链路权重不变，以提高网络的同步性。方向分配已被证明可以提高一般无向网络的同步性，但我们发现，在某些情况下，不可通信的组件出现和网络无法同步。我们发现REBG方法可以有效地避免同步失败（$R=λ_{2}^{r}/λ_{N}^{r}=0$）发生在剩余度梯度（RDG）方法中提出的物理。103，228702（2009）中所述。进一步的实验表明，REBG方法在具有社团结构的网络中比RDG方法提高了同步性。

内在的方向性解释了经验网络中反馈回路的缺乏

Inherent directionality explains the lack of feedback loops in empirical networks

我们探讨的假设，在许多经验复杂网络的反馈回路的相对丰富的严重减少，由于存在一个固有的全球方向性。为了量化这个想法，我们提出了一个简单的概率模型，其中一个自由参数$γ$控制的程度的固有方向性。在加强这种方向性后，该模型预测，也是反馈回路的回路的比例会急剧减少。为了验证这一预测，我们广泛列举了许多经验性生物、生态和社会技术定向网络中的回路和反馈回路。我们发现，在几乎所有情况下，经验网络的反馈回路比网络随机化小得多。非常值得注意的是，这一经验发现是定量再现，所有的环路长度，我们的模型通过拟合其唯一的参数$γ$。此外，$γ$的拟合值与通过新算法执行的网络方向性的另一直接测量相当好地相关。我们的结论是，存在一个固有的网络方向性提供了一个吝啬的定量解释所观察到的经验网络中缺乏反馈回路。