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Highly connected random geometric graphs

2009
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Discrete Applied Mathematics
*

We construct a

doi:10.1016/j.dam.2008.03.001
fatcat:cobjxf3ijvb33apqi3aw2kpj2m
*random**geometric**graph*G n,k by joining each point of P to its k nearest neighbours. ... For many applications it is desirable that G n,k is*highly**connected*, that is, it remains*connected*even after the removal of a small number of its vertices. ... We define the*random**geometric**graph*G n,k by joining each point of P to its k nearest neighbours. Here, and throughout this paper, distance is measured using the Euclidean l 2 norm. ...##
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Probabilistic Properties of Highly Connected Random Geometric Graphs
[chapter]

2018
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Lecture Notes in Computer Science
*

We study reliability in terms of k-edge-

doi:10.1007/978-3-319-74180-2_5
fatcat:c5dgmnfhonampfmpdhc6lg7kaq
*connectivity*in*graphs*. ... These results are then extended to optimal k-edge-*connected*power assignment*graphs*, where we assign transmit power to vertices, and two vertices are*connected*if they both have sufficient transmit power ... Conclusions and Open Problems In this paper, we have looked at fault tolerant networks in terms of k-edge-*connected**graphs*. We studied both a standard (wired) model and a model for wireless networks. ...##
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From Graph Theory to Network Science: The Natural Emergence of Hyperbolicity (Tutorial)

2019
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Symposium on Theoretical Aspects of Computer Science
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Hyperbolic

doi:10.4230/lipics.stacs.2019.5
dblp:conf/stacs/Friedrich19
fatcat:lg4hae3up5a5jfjalfgsvn77hi
*random**graphs*are obtained by choosing*random*points in the hyperbolic plane and*connecting*pairs of points that are*geometrically*close. ... The vertices of a network can be mapped to points in this geometry, such that*geometric*distances are similar to*graph*distances. ... An example of such models are*geometric**random**graphs*[38] (also called*random*unit disk*graphs*). ...##
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Random geometric graphs

2002
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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
*

We analyse

doi:10.1103/physreve.66.016121
pmid:12241440
fatcat:vowbvxkodfhptj7x4bmyqks2ae
*graphs*in which each vertex is assigned*random*coordinates in a*geometric*space of arbitrary dimensionality and only edges between adjacent points are present. ... We derive an analytical expression for the cluster coefficient which shows that the*graphs*are distinctly different from standard*random**graphs*, even for infinite dimensionality. ... A*random**geometric**graph*(RGG) is a*random**graph*with a metric. ...##
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On the Connectivity of Key-Distribution Strategies in Wireless Sensor Networks

2009
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GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference
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In this paper, we study the

doi:10.1109/glocom.2009.5425590
dblp:conf/globecom/ShafieiKTOD09
fatcat:bc724dp2sbdyxnrzvtrfdrdhry
*connectivity*of key-distribution mechanisms in secured topologies of wireless sensor networks. ... We explore the effect of the radio range on the*connectivity*of the network and provide a lower bound on the radio range under which the cover time of the underlying topology decreases significantly. ...*Random**Geometric**Graph*with radio range r 2 (n). ...##
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Multiscale saliency detection for 3D meshes using random walk

2014
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Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2014 Asia-Pacific
*

We perform

doi:10.1109/apsipa.2014.7041602
dblp:conf/apsipa/JeongS14
fatcat:gmqphla4ybgxroucs32v57j3q4
*random*walk on the*graph*and find the stationary distribution of*random*walker, which is used as an initial saliency distribution. ... We construct a weighted undirected*graph*on an input 3D mesh model, by taking the vertices and edges in the mesh as the nodes and links of the*graph*. ... Costa [2] regarded saliency as visiting frequencies of*random*walker to the nodes of a fully*connected**graph*defined on an image. Kim et al. ...##
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Modeling interactome: scale-free or geometric?

2004
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Bioinformatics
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We show that the structure of PPI networks is better modeled by a

doi:10.1093/bioinformatics/bth436
pmid:15284103
fatcat:xhndu5ogejcczg3b67cx4njzr4
*geometric**random**graph*than by a scale-free model. ... We examine the fit of four different network models, including Erdös-Rényi, scalefree, and*geometric**random*network models, to these PPI networks with respect to the measures of local and global network ...*Geometric**Random**Graphs*A*geometric**graph*¥ § ¦ © with radius is a*graph*with node set¨of points in a metric space and edge set ! ...##
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Spectral statistics of random geometric graphs

2017
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Europhysics letters
*

We use

doi:10.1209/0295-5075/118/18003
fatcat:frqft5wd4ben5cpqmwkp24vhmm
*random*matrix theory to study the spectrum of*random**geometric**graphs*, a fundamental model of spatial networks. ... That is the spectral statistics of spatial*random**geometric**graphs*fits the universality of*random*matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert and Watts-Strogatz*random**graph*... Many types of*random**graph*25 models have been analysed, however, the ubiquitous and 26 fundamental class of*geometric**graphs*which are the sim-27 Fig. 1: A*random**geometric**graph*. ...##
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Connectivity in Wireless Ad-hoc Networks with a Log-normal Radio Model

2006
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Journal on spesial topics in mobile networks and applications
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In this paper we study

doi:10.1007/s11036-006-5188-7
fatcat:2hr5am2jtre3lm5kxb7uinqipa
*connectivity*in wireless ad-hoc networks by modeling the network as an undirected*geometric**random**graph*. ... Firstly, they reduce the amount of correlation between links causing the*geometric**random**graph*tend to behave like a*random**graph*with uncorrelated links. ... Therefore we expect our*geometric**random**graph*model to shift between a*highly*clustered regular lattice (for ξ → 0) and a*random**graph*(for highest values of ξ ). ...##
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A curious gap in one-dimensional geometric random graphs between connectivity and the absence of isolated node
[article]

2015
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arXiv
*
pre-print

c ∈( 1/2, 1), a one-dimensional

arXiv:1502.00404v2
fatcat:y4lfhc76qvgqfhuqsq77li4v4y
*geometric**random**graph*has no isolated node but is not*connected*. ... This curious gap in one-dimensional*geometric**random**graphs*is in sharp contrast to the prevalent phenomenon in many other*random**graphs*such as two-dimensional*geometric**random**graphs*, Erdős-Rényi*graphs*...*geometric**random**graphs*. ...##
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Connectivity and Coverage in Hybrid Wireless Sensor Networks using Dynamic Random Geometric Graph Model

2011
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International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks
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In this paper, I study

doi:10.5121/jgraphoc.2011.3304
fatcat:eknfmpojgnbxngx5eaiw4ijrcu
*connectivity*and coverage in hybrid WSN based on dynamic*random**geometric**graph*. ...*Random**Geometric**Graphs*have been a very influential and well-studied model of large networks, such as sensor networks, where the network nodes are represented by the vertices of the RGG, and the direct ... In [1, 13, 18] the authors studied the toplogy and*connectivity*properties of*random**geometric**graphs*. ...##
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A 360-degree Holographic Display System for Radiotherapy Treatment Planning

2015
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Computer-Aided Design and Applications
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It would be parameterized to generate

doi:10.1080/16864360.2015.1114386
fatcat:6hnnhtlwk5cxvmp73s7cvhtp2e
*graphs*with some desirable proprieties, like*highly*or weakly decomposable*graphs*, or restricting the generated*graph*to a specific class of*geometric*configuration ... Each one is solved, separately, and the final solution is obtained by recomposing the solved sub-*graphs*. To the best of our knowledge, there is no*random**geometric*constraint*graph*generator so far. ... G 6. replace the edge (x, y) by the*graph*H as follows: 7. pick two*random*vertices x' and y' from the*graph*H 8.*connect*x', to all neighbours of x 9.*connect*y', to all neighbours of y 10. delete x ...##
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Scale-invariant geometric random graphs

2016
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Physical review. E
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We introduce and analyze a class of growing

doi:10.1103/physreve.93.032310
pmid:27078369
fatcat:ebpovmv2yzbotkf2iqnavim2za
*geometric**random**graphs*that are invariant under rescaling of space and time. ... Through calculations and numerical simulations we explore the consequences of scale-invariance for*geometric**random**graphs*generated this way. ... Minkowski space), it becomes possible to discuss dynamical*random**geometric**graphs*. ...##
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Introduction to the Special Issue on AI and Networks

2008
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The AI Magazine
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AI Magazine's Special Issueon Networks and AI summarizes the seven articles in thespecial issue by characterizing the nature of thenetworks that are the focus of each of the papers.A short tutorial on

doi:10.1609/aimag.v29i3.2163
fatcat:jbo5srk5kzgsnircweu7zp3ezm
*graph*... A*random**geometric**graph*is a special case of a*random**graph*that is generated by randomly placing N agents in the unit square, then*connecting*pairs of agents if they are within some specified distance ... More specifically, two agents, i and j are*connected*in a*random**geometric**graph*if d(i, j) < φ, where φ is a threshold parameter of the model. ...##
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Enhanced Random Walk with Choice: An Empirical Study
[article]

2010
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arXiv
*
pre-print

Simulation results show a significant improvement in cover time, maximum node load and load balancing, mainly in

arXiv:1007.3157v1
fatcat:ffhvrojtlbchvlrfq235jgm6sa
*random**geometric**graphs*. ... We compare the*random*walk with choice with its enhanced counterpart. ... The best known cases correspond to dense,*highly**connected**graphs*; on the other hand, when*connectivity*decreases and bottlenecks exist in the*graph*, the cover time increases. ...
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