Expansion in matrix-weighted graphs
| Autor: | Jakob Hansen |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Positive-definite matrix Edge (geometry) Graph Mathematics - Spectral Theory Combinatorics Matrix (mathematics) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Expander graph Combinatorics (math.CO) Geometry and Topology Adjacency matrix Spectral Theory (math.SP) Laplace operator Expander mixing lemma Mathematics |
| Zdroj: | Linear Algebra and its Applications. 630:252-273 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2021.08.009 |
| Popis: | A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to define and control expansion for matrix-weighted graphs. In particular, an analogue of the expander mixing lemma and one half of a Cheeger-type inequality hold for matrix-weighted graphs. A new definition of a matrix-weighted expander graph suggests the tantalizing possibility of families of matrix-weighted graphs with better-than-Ramanujan expansion. 21 pages, 2 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect