Interconnecting strategy of bridging multilayer networks to maximize synchronizability

¹ School of Economics and Management, Southwest Jiaotong University - Chengdu, 610031, China
² Service Science and Innovation Key Lab of Sichuan Province - Chengdu 610031, China
³ School of Electrical Engineering and Automation, Jiangsu Normal University - Xuzhou 221116, China
⁴ Cybersecurity Research Institute, Sichuan University - Chengdu 610065, China

^(a) wwzqbx@hotmail.com (corresponding author)

Received: 25 November 2018
Accepted: 4 January 2019

Abstract

Since many real-world system are described as multilayer networks, researchers focus their efforts on the subject of synchronization of multilayer networks. In this paper, we propose an strategy of bridging multilayer networks with p-links to get the maximum synchronizability. Based on the matrix perturbation theory, the problem of placing p-links between any two networks is transformed into p-times placing one-link structure perturbation to the original Laplacian matrix problem. Instead of exhaustive searching in the infinite space, we break the complicated problem into p sub-problem. In each sub-problem, we just need to sort two vectors and choose the maximum elements as the interconnecting node pair. This method significantly reduces the computing burden. To verify the effectiveness of our strategy, we perform some simulations to compare our method with other strategies. The results show that our strategies outperforms in most cases.