# 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}
}
• Published 2015
• Computer Science, Physics, Mathematics
• 2015 IEEE International Conference on Communications (ICC)
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… Expand
From the betweenness centrality in street networks to structural invariants in random planar graphs
• Mathematics, Medicine
• Nature 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. Expand
Betweenness centrality in dense spatial networks
• Computer Science, Physics
• ArXiv
• 2021
The lowest non-trivial order is computed and it is shown that it encodes how straight are shortest paths and is therefore non-universal and depends on the graph considered. Expand
Shape of shortest paths in random spatial networks.
• Medicine, Physics
• Physical 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. Expand
Structural invariants in street networks: modeling and practical implications
• Mathematics
• 2017
We study structural properties of street networks from 97 of the most populous cities worldwide at scales significantly larger than previous studies. We find that the distribution of betweennessExpand
Euclidean Matchings in Ultra-Dense Networks
• Mathematics, Physics
• IEEE 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. Expand
Connectivity of Soft Random Geometric Graphs over Annuli
• Computer Science, Mathematics
• 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 ofExpand
Meta Distribution of SIR in Ultra-Dense Networks with Bipartite Euclidean Matchings
• Mathematics, Computer Science
• ICC 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. Expand
Connectivity of 1d random geometric graphs
• Computer Science, Mathematics
• ArXiv
• 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. Expand
Connectivity and Centrality in Dense Random Geometric Graphs
Due to shorter range communication becoming more prevalent with the development of multiple-input, multiple-output antennas (MIMO) and millimeter wave communications, multi-hop, intra-cellExpand
How does mobility affect the connectivity of interference-limited ad hoc networks?
• Computer Science, Mathematics
• 2016 14th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)
• 2016
This paper will use the well established Random Waypoint Mobility Model (RWPM) to represent such a network of mobile devices, and show that the connectivity of a receiver at different parts of the network domain varies significantly. Expand

#### References

SHOWING 1-10 OF 27 REFERENCES
Centrality scaling in large networks.
• Computer Science, Physics
• Physical review letters
• 2010
A multiscale decomposition of shortest paths shows that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling versus L, which can be used to predict the distribution of the full centralities. Expand
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
• Computer Science
• IEEE Trans. Mob. Comput.
• 2003
The critical transmitting range for connectivity in wireless ad hoc networks is analyzed and insight into how mobility affects connectivity is yielded and useful trade offs between communication capability and energy consumption are revealed. Expand
Vulnerability of weighted networks
• Physics
• 2006
In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may also play an importantExpand
CONNECTIVITY OF SOFT RANDOM GEOMETRIC GRAPHS
Consider a graph on $n$ uniform random points in the unit square, each pair being connected by an edge with probability $p$ if the inter-point distance is at most $r$. We show that as $n \to \infty$Expand
Stochastic geometry and random graphs for the analysis and design of wireless networks
• Computer Science
• IEEE Journal on Selected Areas in Communications
• 2009
This tutorial article surveys some of these techniques based on stochastic geometry and the theory of random geometric graphs, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. Expand
Network connectivity: Stochastic vs. deterministic wireless channels
• Computer Science, Mathematics
• 2014 IEEE International Conference on Communications (ICC)
• 2014
Analysis of local and global network observables presents conclusive evidence suggesting that network behaviour is highly dependent upon whether a stochastic or deterministic connection model is employed, and shows that the network mean degree is lower for Stochastic wireless channels than for deterministic ones, if the path loss exponent is greater than the spatial dimension. Expand
Attack vulnerability of complex networks.
• Mathematics, Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics
• 2002
It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed. Expand
Boundary recognition in sensor networks by topological methods
• Computer Science
• MobiCom '06
• 2006
This paper proposes a simple, distributed algorithm that correctly detects nodes on the boundaries and connects them into meaningful boundary cycles, and obtains as a byproduct the medial axis of the sensor field, which has applications in creating virtual coordinates for routing. Expand
A faster algorithm for betweenness centrality
Motivated by the fast‐growing need to compute centrality indices on large, yet very sparse, networks, new algorithms for betweenness are introduced in this paper. They require O(n + m) space and runExpand
Impact of boundaries on fully connected random geometric networks
• Mathematics, Computer Science
• Physical review. E, Statistical, nonlinear, and soft matter physics
• 2012
This work correctly distinguishes connectivity properties of networks in domains with equal bulk contributions and facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension. Expand