Enhancing the spectral gap of networks by node removal

TL;DR

This paper proposes a perturbative method to enhance the spectral gap of networks by node removal, improving network performance metrics like synchronization and convergence speed.

Contribution

A novel perturbative approach for increasing the spectral gap through node removal, outperforming heuristic methods on various networks.

Findings

Spectral gap increases significantly with node removal up to half the nodes.

The method outperforms other heuristic strategies.

Applicable to both model and real-world networks.

Abstract

Dynamics on networks are often characterized by the second smallest eigenvalue of the Laplacian matrix of the network, which is called the spectral gap. Examples include the threshold coupling strength for synchronization and the relaxation time of a random walk. A large spectral gap is usually associated with high network performance, such as facilitated synchronization and rapid convergence. In this study, we seek to enhance the spectral gap of undirected and unweighted networks by removing nodes because, practically, the removal of nodes often costs less than the addition of nodes, addition of links, and rewiring of links. In particular, we develop a perturbative method to achieve this goal. The proposed method realizes better performance than other heuristic methods on various model and real networks. The spectral gap increases as we remove up to half the nodes in most of these networks.