How to improve network connectivity and which parts of the network are vulnerable are critical issues. We begin by defining an equal distribution problem, in which supplies are distributed equally to all nodes in the network. We then derive a topological network connectivity measure from the convergence speed, which is the second minimum eigenvalue of a Laplacian network matrix. Based on the equal distribution problem, we propose a method for identifying critical links for network connectivity using the derivative of the second minimum eigenvalue. Furthermore, we develop a network design problem that maximizes topological connectivity within a budget creating strengthening network links. The problem is convex programming, and the solution is global. Furthermore, it can be converted into an identical semidefinite programming problem, which requires less computational effort. Finally, we test the developed problems on road networks in the Japanese prefectures of Ishikawa and Toyama to determine their applicability and validity.

中文翻译：

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基于频谱分析的拓扑网络连接设计问题


如何改善网络连接以及网络的哪些部分容易受到攻击是关键问题。我们首先定义一个平均分配问题，其中供应平均分配给网络中的所有节点。然后，我们从收敛速度中推导出拓扑网络连通性度量，这是拉普拉斯网络矩阵的第二个最小特征值。基于等分布问题，我们提出了一种使用第二个最小特征值的导数来识别网络连接关键链接的方法。此外，我们开发了一个网络设计问题，在预算内最大限度地提高拓扑连接性，从而创建更强大的网络链接。问题是凸编程，解决方案是全局的。此外，它可以转换为相同的半定规划问题，这需要更少的计算工作量。最后，我们在日本石川县和富山县的道路网络上测试了开发的问题，以确定它们的适用性和有效性。