Dynamical network size estimation from local observations

• Published in: New journal of physics Vol. 22; no. 9; pp. 93031 - 93038
• Main Authors: Tang, Xiuchuan, Huo, Wei, Yuan, Ye, Li, Xiuting, Shi, Ling, Ding, Han, Kurths, Jürgen
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01-09-2020
• Subjects: Algorithms; Computer simulation; dynamical system; Hankel matrix; network size; Physics
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/abaf2f

Here we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks.