# Betweenness centrality in dense random geometric networks

@article{Giles2015BetweennessCI, title={Betweenness centrality in dense random geometric networks}, author={Alexander P. Giles and Orestis Georgiou and Carl P. Dettmann}, journal={2015 IEEE International Conference on Communications (ICC)}, year={2015}, pages={6450-6455} }

Random geometric networks are mathematical structures consisting of a set of nodes placed randomly within a bounded set V ⊆ ℝd mutually coupled with a probability dependent on their Euclidean separation, and are the classic model used within the expanding field of ad hoc wireless networks. In order to rank the importance of the network's communicating nodes, we consider the well established `betweenness' centrality measure (quantifying how often a node is on a shortest path of links between any…

## 21 Citations

From the betweenness centrality in street networks to structural invariants in random planar graphs

- Computer ScienceNature Communications
- 2018

The results suggest that the spatial distribution of betweenness is a more accurate discriminator than its statistics for comparing static congestion patterns and its evolution across cities as demonstrated by analyzing 200 years of street data for Paris.

Betweenness centrality in dense spatial networks

- Computer SciencePhysical review. E
- 2022

This work compute the lowest nontrivial order and shows that it encodes how straight are shortest paths and is therefore nonuniversal and depends on the graph considered, and compares the analytical result to numerical simulations obtained for various graphs.

Shape of shortest paths in random spatial networks.

- MathematicsPhysical review. E
- 2019

The results shed some light on the Euclidean first-passage process but also raise some theoretical questions about the scaling laws and the derivation of the exponent values and also whether a model can be constructed with maximal wandering, or non-Gaussian travel fluctuations, while embedded in space.

Structural invariants in street networks: modeling and practical implications

- Computer Science
- 2017

The distribution of betweenness centrality (BC) is invariant in all studied street networks, despite the obvious structural differences between them, indicating that the only relevant factors shaping the distribution are the number of nodes in a network, theNumber of edges, and the constraint of planarity.

Euclidean Matchings in Ultra-Dense Networks

- Computer ScienceIEEE Communications Letters
- 2018

This work studies the spatial spectral efficiency gain achieved when communication devices densely embedded in the d-dimensional Euclidean plane are optimally matched in near-neighbor pairs, and deriving the scaling limit of both models using the replica method from the physics of disordered systems.

Connectivity of Soft Random Geometric Graphs over Annuli

- Computer Science
- 2016

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of…

Meta Distribution of SIR in the Internet of Things Modelled as a Euclidean Matching

- Computer Science
- 2019

How the widely-accepted bipolar model fails to capture the network-wide reliability of communication in a typical ultra-dense setting based on a binomial point process is illustrated and how assuming a Gamma distribution for link distances may be a simple improvement on the bipolar model is shown.

Meta Distribution of SIR in Ultra-Dense Networks with Bipartite Euclidean Matchings

- MathematicsICC 2019
- 2019

This paper studies how a bipartite Euclidean matching can be used to investigate the reliability of communication in interference-limited ultra-dense networks, and asks how the new matching idea effectively leads to variable link distances, a factor not typically incorporated in meta distribution studies.

Connectivity of 1d random geometric graphs

- MathematicsArXiv
- 2021

An important link between spatial random graphs, and lattice path combinatorics, where the d-dimensional lattice paths correspond to spatial permutations of the geometric points on the line is demonstrated and described.

Connectivity and Centrality in Dense Random Geometric Graphs

- Computer Science
- 2016

This analysis involves a stochastic spatial network model called a random geometric graph, which is used to model a network of interconnected devices communicating wirelessly without any separate, pre-established infrastructure.

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