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.