Incremental eigenpair computation for graph Laplacian matrices: theory and applications

Incremental Computation of Pseudo-Inverse of Laplacian: Theory and Applications

A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix (L) of a simple, undirected graph is proposed. The nature of the underlying sub-problems is studied in detail by means of an elegant interplay between L and the effective resistance distance (Ω). Closed forms are provided for a novel two-stage process that helps compute the p...

Algorithms, Graph Theory, and Linear Equations in Laplacian Matrices

The Laplacian matrices of graphs are fundamental. In addition to facilitating the application of linear algebra to graph theory, they arise in many practical problems. In this talk we survey recent progress on the design of provably fast algorithms for solving linear equations in the Laplacian matrices of graphs. These algorithms motivate and rely upon fascinating primitives in graph theory, in...

Incremental Computation of Pseudo-Inverse of Laplacian

A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix (L) of a simple, undirected graph is proposed. The nature of the underlying sub-problems is studied in detail by means of an elegant interplay between L and the effective resistance distance (Ω). Closed forms are provided for a novel two-stage process that helps compute the p...

Matrices: Theory and Applications

MAT 280: Laplacian Eigenfunctions: Theory, Applications, and Computations Lecture 20: Introduction to Spectral Graph Theory–III. Graph Cut and Cheeger Constants, Isospectral Graphs, and Discrete Laplacian Eigenvalue Problems

Example 1.2. In Figure 1, S is the set of dark nodes, and the dotted lines form ∂S. S ∆ = V \S. Also, vol(S) = m(S) ∆ = x∈S m(x).