English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We discuss a Cheeger constant as a mixture of the frustration index and theexpansion rate, and prove the related Cheeger inequalities and higher orderCheeger inequalities for graph Laplacians with cyclic signatures, discretemagnetic Laplacians on finite graphs and magnetic Laplacians on closedRiemannian manifolds. In this process, we develop spectral clusteringalgorithms for partially oriented graphs and multi-way spectral clusteringalgorithms via metrics in lens spaces and complex projective spaces. As abyproduct, we give a unified viewpoint of Harary's structural balance theory ofsigned graphs and the gauge invariance of magnetic potentials.

Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians