Effective resistance is more than distance: Laplacians, Simplices and the Schur complement

This article reviews and discusses a geometric perspective on the well-known fact in graph theory that effective resistance is metric nodes of graph. The classical proofs this make use ideas from electrical circuits or random walks; here we describe an alternative approach which combines (using simplices) algebraic Schur complement) ideas. These perspectives are unified matrix identity Miroslav Fiedler, beautifully summarizes number related at intersection graphs, Laplacian matrices simplices, with property as prominent consequence.