Betweenness centrality in dense random geometric networks

  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)},
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… 

Figures from this paper

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


Centrality scaling in large networks.
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.
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
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.
Vulnerability of weighted networks
The analysis of weighted properties shows that centrality driven attacks are capable of shattering the network’s communication or transport properties even at a very low level of damage in the connectivity pattern and the inclusion of weight and traffic provides evidence for the extreme vulnerability of complex networks to any targeted strategy.
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 $n \to \infty$
Stochastic geometry and random graphs for the analysis and design of wireless networks
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.
Network connectivity: Stochastic vs. deterministic wireless channels
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.
Attack vulnerability of complex networks.
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.
Boundary recognition in sensor networks by topological methods
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.
A faster algorithm for betweenness centrality
New algorithms for betweenness are introduced in this paper and require O(n + m) space and run in O(nm) and O( nm + n2 log n) time on unweighted and weighted networks, respectively, where m is the number of links.
Impact of boundaries on fully connected random geometric networks
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.