Geometrical and spectral study of beta-skeleton graphs

Alonso, Lázaro; Mendez-Bermudez, J. A.; Estrada, Ernesto

doi:10.1103/PhysRevE.100.062309

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Geometrical and spectral study of beta-skeleton graphs

MPS-Authors

/persons/resource/persons246559

Alonso, Lázaro
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

1907.07262.pdf
(Preprint), 2MB

Supplementary Material (public)

There is no public supplementary material available

Citation

Alonso, L., Mendez-Bermudez, J. A., & Estrada, E. (2019). Geometrical and spectral study of beta-skeleton graphs. Physical Review E, 100(6): 062309. doi:10.1103/PhysRevE.100.062309.

Cite as: https://hdl.handle.net/21.11116/0000-0005-DFCF-8

Abstract

We perform an extensive numerical analysis of beta-skeleton graphs, a particular type of proximity graphs. In beta-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter beta is an element of (0, infinity), is satisfied. Moreover, for beta > 1 there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of beta, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of random BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at beta = 1.