The role of nodes in controlling and observing complex networks

Abstract

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⃼