A generalized Cheeger inequality
Document Type
Article
Publication Date
5-15-2023
Abstract
The generalized conductance ϕ(G,H) between two weighted graphs G and H on the same vertex set V is defined as the ratio [Formula presented] where capG(S,S¯) is the total weight of the edges crossing from vertex set S⊆V to S¯=V−S. We show that the minimum generalized eigenvalue λ(LG,LH) of the pair of Laplacians LG and LH satisfies ϕ(G,H)≥λ(LG,LH)≥ϕ(G,H)ϕ(G)/16, where ϕ(G) is the standard conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to λ(LG,LH).
Identifier
85147999385 (Scopus)
Publication Title
Linear Algebra and Its Applications
External Full Text Location
https://doi.org/10.1016/j.laa.2023.01.014
ISSN
00243795
First Page
139
Last Page
152
Volume
665
Grant
2039863
Fund Ref
National Science Foundation
Recommended Citation
Koutis, Ioannis; Miller, Gary; and Peng, Richard, "A generalized Cheeger inequality" (2023). Faculty Publications. 1727.
https://digitalcommons.njit.edu/fac_pubs/1727
