Sunflower hard disk graphs

Carl P Dettmann; Orestis Georgiou

doi:10.1016/j.physa.2023.129180

Sunflower hard disk graphs

Carl P Dettmann ^*, Orestis Georgiou

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

The random geometric graph consists of a random point set with links between points with mutual distance below a fixed threshold. Here, we use the same geometric connection rule (“hard disk graph”) but for a deterministic point set, the sunflower spiral. At large distances, the local structure is asymptotically a lattice where for each lattice vector, there is another of length a factor√5 greater, and the angle between these varies log-periodically with distance from the origin. Graph properties including node degrees, stretch factor, clique and chromatic numbers are considered, as well as link formation, connectivity and planarity transitions. Properties depend on a combination of the central region and the perturbed distant lattices, in a rich and varied manner.

Original language	English
Article number	129180
Number of pages	15
Journal	Physica A: Statistical Mechanics and its Applications
Volume	629
Early online date	3 Sept 2023
DOIs	https://doi.org/10.1016/j.physa.2023.129180
Publication status	Published - 1 Nov 2023

Bibliographical note

Funding Information:
This work was supported by the Engineering and Physical Sciences Research Council [ EP/N002458/1 ]. All underlying data is included in full within the paper.

Publisher Copyright:
© 2023 The University of Bristol

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Dettmann , C. P. (Principal Investigator)
1/11/15 → 18/03/19
Project: Research

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title = "Sunflower hard disk graphs",

abstract = "The random geometric graph consists of a random point set with links between points with mutual distance below a fixed threshold. Here, we use the same geometric connection rule (“hard disk graph”) but for a deterministic point set, the sunflower spiral. At large distances, the local structure is asymptotically a lattice where for each lattice vector, there is another of length a factor√5 greater, and the angle between these varies log-periodically with distance from the origin. Graph properties including node degrees, stretch factor, clique and chromatic numbers are considered, as well as link formation, connectivity and planarity transitions. Properties depend on a combination of the central region and the perturbed distant lattices, in a rich and varied manner.",

author = "Dettmann, \{Carl P\} and Orestis Georgiou",

note = "Funding Information: This work was supported by the Engineering and Physical Sciences Research Council [ EP/N002458/1 ]. All underlying data is included in full within the paper. Publisher Copyright: {\textcopyright} 2023 The University of Bristol",

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doi = "10.1016/j.physa.2023.129180",

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AU - Dettmann , Carl P

AU - Georgiou, Orestis

N1 - Funding Information: This work was supported by the Engineering and Physical Sciences Research Council [ EP/N002458/1 ]. All underlying data is included in full within the paper. Publisher Copyright: © 2023 The University of Bristol

PY - 2023/11/1

Y1 - 2023/11/1

N2 - The random geometric graph consists of a random point set with links between points with mutual distance below a fixed threshold. Here, we use the same geometric connection rule (“hard disk graph”) but for a deterministic point set, the sunflower spiral. At large distances, the local structure is asymptotically a lattice where for each lattice vector, there is another of length a factor√5 greater, and the angle between these varies log-periodically with distance from the origin. Graph properties including node degrees, stretch factor, clique and chromatic numbers are considered, as well as link formation, connectivity and planarity transitions. Properties depend on a combination of the central region and the perturbed distant lattices, in a rich and varied manner.

AB - The random geometric graph consists of a random point set with links between points with mutual distance below a fixed threshold. Here, we use the same geometric connection rule (“hard disk graph”) but for a deterministic point set, the sunflower spiral. At large distances, the local structure is asymptotically a lattice where for each lattice vector, there is another of length a factor√5 greater, and the angle between these varies log-periodically with distance from the origin. Graph properties including node degrees, stretch factor, clique and chromatic numbers are considered, as well as link formation, connectivity and planarity transitions. Properties depend on a combination of the central region and the perturbed distant lattices, in a rich and varied manner.

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DO - 10.1016/j.physa.2023.129180

M3 - Article (Academic Journal)

SN - 0378-4371

VL - 629

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 129180

ER -

Sunflower hard disk graphs

Abstract

Bibliographical note

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