通过节点移除来增强网络的谱间隙
Enhancing the spectral gap of networks by node removal
摘要：
网络的动力学通常由网络的拉普拉斯矩阵的第二小特征值来表征，这被称为谱隙。例子包括用于同步的阈值耦合强度和随机游走的弛豫时间。大的频谱间隙通常与高的网络性能相关联，例如促进同步和快速收敛。在这项研究中，我们试图通过删除节点来增强无向和无权网络的谱隙，因为实际上，删除节点的成本往往低于添加节点，添加链接和重新布线的链接。特别是，我们开发了一种微扰方法来实现这一目标。该方法在各种模型和实际网络上都取得了比其他启发式方法更好的性能。在大多数网络中，当我们删除一半的节点时，频谱间隙会增加。
英文摘要：
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.
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