论文标题
有效的阻力不仅仅是距离：拉普拉斯人，简单和舒尔补体
Effective resistance is more than distance: Laplacians, Simplices and the Schur complement
论文作者
论文摘要
本文讨论了图理论中众所周知的事实的几何观点，即有效抗性是图表上的一个度量。这一事实的经典证据利用了电路或随机步行的想法；在这里，我们描述了一种替代方法，该方法结合了几何（使用简单）和代数（使用Schur补充）思想。这些观点是在米罗斯拉夫·菲德勒（Miroslav Fiedler）的矩阵身份中统一的，在图形，拉普拉斯（Laplacian）矩阵和简单的相交中，它以有效阻力的指标为重要的后果，总结了许多相关的想法。
This article discusses a geometric perspective on the well-known fact in graph theory that the effective resistance is a metric on the nodes of a graph. The classical proofs of this fact make use of ideas from electrical circuits or random walks; here we describe an alternative approach which combines geometric (using simplices) and algebraic (using the Schur complement) ideas. These perspectives are unified in a matrix identity of Miroslav Fiedler, which beautifully summarizes a number of related ideas at the intersection of graphs, Laplacian matrices and simplices, with the metric property of the effective resistance as a prominent consequence.
