Wu Longlong
School of Electromechanical Engineering, Jiangxi Vocational and Technical College of Communication, Nanchang, China.
PLoS One. 2025 Jun 12;20(6):e0325824. doi: 10.1371/journal.pone.0325824. eCollection 2025.
Dynamic processes on complex networks are closely associated with a variety of real-world systems. The controllability and observability of these networks are critical topics in the field of network science. Motivated by recent advancements in the study of structural controllability and observability, we investigate the roles of nodes in controlling and observing complex networks. Specifically, we categorize individual nodes into one of four types: driver nodes, sensor nodes, dual-identity nodes, and ordinary nodes. We propose a general framework for identifying the category of each node, thereby facilitating the exploration of the structural characteristics of these node types. Our findings indicate that these four types of nodes are prevalent in the control and observation of real networks. Through the analysis of their structural characteristics, we observe that nodes involved in controllability and observability are more likely to be low-degree nodes. Furthermore, we show that the proportions of these node categories are largely governed by the degree distribution of the network. Additionally, we present a theoretical analytical method to derive the proportions of the four node types, based on the network's degree distribution.
复杂网络上的动态过程与各种现实世界系统密切相关。这些网络的可控性和可观测性是网络科学领域的关键课题。受结构可控性和可观测性研究近期进展的启发，我们研究节点在控制和观测复杂网络中的作用。具体而言，我们将单个节点分为四种类型之一：驱动节点、传感节点、双重身份节点和普通节点。我们提出了一个用于识别每个节点类别的通用框架，从而便于探索这些节点类型的结构特征。我们的研究结果表明，这四种类型的节点在实际网络的控制和观测中普遍存在。通过对其结构特征的分析，我们观察到参与可控性和可观测性的节点更有可能是低度节点。此外，我们表明这些节点类别的比例在很大程度上由网络的度分布决定。此外，我们提出了一种理论分析方法，基于网络的度分布来推导四种节点类型的比例。
