A generalized Cheeger inequality
نویسندگان
چکیده
The generalized conductance ϕ(G,H) between two weighted graphs G and H on the same vertex set V is defined as ratioϕ(G,H)=minS⊆VcapG(S,S¯)capH(S,S¯), where capG(S,S¯) total weight of edges crossing from S⊆V to S¯=V−S. We show that minimum eigenvalue λ(LG,LH) pair Laplacians LG LH satisfiesϕ(G,H)≥λ(LG,LH)≥ϕ(G,H)ϕ(G)/16, ϕ(G) standard G. A cut meets this bound can be obtained eigenvector corresponding λ(LG,LH).
منابع مشابه
A Generalized Cheeger Inequality
where capG(S, S̄) is the total weight of the edges crossing from S to S̄ = V − S. We show that the minimum generalized eigenvalue λ(LG, LH) of the pair of Laplacians LG and LH satisfies λ(LG, LH) ≥ φ(G,H)φ(G)/8, where φ(G) is the usual conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to λ(LG, LH). The inequality complements a...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2023
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2023.01.014