title: Enhancing the spectral gap of networks by node removal.
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.
authors.affiliation: Department of Physiology, School of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
authors.forename: Takamitsu
authors.initials: T
authors.lastname: Watanabe
authors.forename: Naoki
authors.initials: N
authors.lastname: Masuda
mesh_terms: D000818:Animals; D017173:Caenorhabditis elegans / Q000166:cytology; D034742:Electronic Mail; D004926:Escherichia coli / Q000378:metabolism; D008251:Macaca; D053858:Metabolic Networks and Pathways; D008962:Models, Theoretical; D009415:Nerve Net / Q000166:cytology / Q000378:metabolism; D012944:Social Support