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首页> 外文期刊>IEEE Transactions on Automatic Control >A New Notion of Effective Resistance for Directed Graphs—Part I: Definition and Properties
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A New Notion of Effective Resistance for Directed Graphs—Part I: Definition and Properties

机译：有向图的有效抵抗力的新概念-第一部分：定义和性质

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摘要

The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in undirected graphs and yet in several areas of its application, directed graphs arise as naturally (or more naturally) than undirected ones. In Part I of this work, we propose a generalization of effective resistance to directed graphs that preserves its control-theoretic properties in relation to consensus-type dynamics. We proceed to analyze the dependence of our algebraic definition on the structural properties of the graph and the relationship between our construction and a graphical distance. The results make possible the calculation of effective resistance between any two nodes in any directed graph and provide a solid foundation for the application of effective resistance to problems involving directed graphs.
机译：有效电阻的图形概念已在纯数学，应用数学和控制理论的许多领域中得到了广泛的应用。根据其构造的性质，只能在无向图中计算有效电阻，但是在其应用的几个领域中，有向图比无向图自然（或更自然）地出现。在这项工作的第一部分中，我们提出了对有向图的有效抵抗的概括，保留了其与共识类型动力学有关的控制理论特性。我们继续分析代数定义对图的结构特性以及构造与图形距离之间关系的依赖性。结果使计算任何有向图的任意两个节点之间的有效电阻成为可能，并为将有效电阻应用于涉及有向图的问题提供了坚实的基础。

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