Rodgers Niall, Tiňo Peter, Johnson Samuel
School of Mathematics, University of Birmingham, Birmingham, UK.
Topological Design Centre for Doctoral Training, University of Birmingham, Birmingham, UK.
R Soc Open Sci. 2023 Aug 30;10(8):221380. doi: 10.1098/rsos.221380. eCollection 2023 Aug.
Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of trophic analysis to study directed networks and show that both 'influence' and 'influenceability' in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localizes; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalized rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted-that node hierarchy is essential for understanding network influence, mediated by global directionality-are applicable to many real-world dynamics.
了解复杂网络中哪些节点具有影响力以及该网络是否能受到一小部分节点的影响是网络分析的关键部分。然而，许多传统的重要性度量方法侧重于节点层面的信息，而未考虑全局网络架构。我们使用营养分析方法来研究有向网络，并表明有向网络中的“影响力”和“可影响性”分别取决于由营养层级和营养一致性所衡量的层次结构和全局方向性。我们表明，在有向网络中，营养层级能够解释：能够到达最多其他节点的节点；特征向量中心性集中的位置；在意见或振荡器动力学中塑造行为的节点；以及在广义石头剪刀布游戏中哪些策略会成功。此外，我们表明这些现象是由全局方向性介导的。我们还强调了与可影响性相关的真实网络的其他结构属性，例如依赖于营养一致性的伪谱。这些结果适用于任何有向网络，并且所强调的原则——即节点层次结构对于理解由全局方向性介导的网络影响至关重要——适用于许多现实世界的动态过程。
