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Dynamic Random Geometric Graphs [article]

Josep Diaz, Dieter Mitsche, Xavier Perez
2007 arXiv   pre-print
random geometric graphs.  ...  In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static  ...  We denote this graph model the Dynamic Random Geometric Graph.  ... 
arXiv:cs/0702074v2 fatcat:fw5oumydgzewbnl4mkrszggmba

Opinion Dynamics and Influencing on Random Geometric Graphs

Weituo Zhang, Chjan C. Lim, G. Korniss, Boleslaw K. Szymanski
2014 Scientific Reports  
We investigate the two-word Naming Game on two-dimensional random geometric graphs.  ...  Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics.  ...  Random geometric graph consists of N agents randomly distributed in a unit square D = [0, 1) 2 .  ... 
doi:10.1038/srep05568 pmid:24993655 pmcid:PMC4081874 fatcat:lxgbszktajgnxn4zmav75laig4

Markov Random Geometric Graph (MRGG): A Growth Model for Temporal Dynamic Networks [article]

Yohann de Castro
2021 arXiv   pre-print
We introduce Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks.  ...  It is based on a Markovian latent space dynamic: consecutive latent points are sampled on the Euclidean Sphere using an unknown Markov kernel; and two nodes are connected with a probability depending on  ...  In (Díaz et al., 2008) , the expected length of connectivity and dis-connectivity periods of the Dynamic Random Geometric Graph is studied: each node choose at random an angle in [0, 2π) and make a constant  ... 
arXiv:2006.07001v2 fatcat:ltuuw4s44jbsfbq67yoejm7wpm

Zero-One Law for Connectivity in Superposition of Random Key Graphs on Random Geometric Graphs

Y. Tang, Q. L. Li
2015 Discrete Dynamics in Nature and Society  
We study connectivity property in the superposition of random key graph on random geometric graph.  ...  For this class of random graphs, we establish a new version of a conjectured zero-one law for graph connectivity as the number of nodes becomes unboundedly large.  ...  Condition 1 produces a random geometric graph with the transmission range .  ... 
doi:10.1155/2015/982094 fatcat:o72dtzp34ncszl2cyly4njx5q4

Markov random geometric graph, MRGG: A growth model for temporal dynamic networks

Quentin Duchemin, Yohann De Castro
2022 Electronic Journal of Statistics  
We introduce Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks.  ...  As a by product, we show how MRGGs can be used to detect dependence structure in growing graphs and to solve link prediction problems.  ...  https://github.com/quentin-duchemin/Markovian-random-geometric-graph  ... 
doi:10.1214/21-ejs1969 fatcat:h55vpjozyrax5gq4pasewvq7ee

Connectivity and Coverage in Hybrid Wireless Sensor Networks using Dynamic Random Geometric Graph Model

Jasmine Norman
2011 International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks  
In this paper, I study 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  ...  A natural candidate for random network modeling is the class of Random Geometric Graphs [8] .  ... 
doi:10.5121/jgraphoc.2011.3304 fatcat:eknfmpojgnbxngx5eaiw4ijrcu

Isolation statistics in temporal spatial networks

Carl P. Dettmann, Orestis Georgiou
2017 Europhysics letters  
We consider soft random geometric graphs, constructed by distributing points (nodes) randomly according to a Poisson Point Process, and forming links between pairs of nodes with a probability that depends  ...  Keeping the node locations fixed, the links break and reform over time, making a dynamic network; this is a good model of a wireless ad-hoc network with communication channels undergoing rapid fading.  ...  If the link probability is one for |ξ − ξ | ≤ 1 and zero otherwise, the only source of randomness is in the node locations. This is the original random geometric graph (RGG) model [22] .  ... 
doi:10.1209/0295-5075/119/28002 fatcat:ynmjaq447jdkrjnkxo6oo2uele

Large Scale Simulations of a Neural Network Model for the Graph Bisection Problem on Geometrically Connected Graphs

Gonzalo Hernandez, Luis Salinas
2004 Electronic Notes in Discrete Mathematics  
In this work some preliminary numerical results obtained by large scale simulations of the sequential dynamics of a neural network model for the graph bisection problem on random geometrically connected  ...  It can be concluded that the sequential dynamic is a low cost, effective and very fast local minima optimization heuristic for the Graph Bisection Problem.  ...  over all the random geometrically connected graphs and initial conditions.  ... 
doi:10.1016/j.endm.2004.06.024 fatcat:7njsxz3v3vaxhbrzlhuiwqy6q4

Navigability of Random Geometric Graphs in the Universe and Other Spacetimes

William Cunningham, Konstantin Zuev, Dmitri Krioukov
2017 Scientific Reports  
Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions  ...  This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs.  ...  The boxplots summarize the distributions of the success ratio (a) and stretch (b) as functions of the number N p of random source-destination node pairs sampled in 10 random geometric graphs (N p pair  ... 
doi:10.1038/s41598-017-08872-4 pmid:28821852 pmcid:PMC5562713 fatcat:bt7opgo5vvc7hh726jsqm324nq

Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity

E. Capiez-Lernout, C. Soize, M. Mbaye
2015 Journal of Sound and Vibration  
The random nature of the mistuning is then modeled by using the nonparametric probabilistic approach extended to the nonlinear geometric context.  ...  Secondly, a detailed dynamic analysis and uncertainty propagation are conducted in order to quantify the impact of the nonlinear geometrical effects on the mistuned structure.  ...  As commonly observed, this graph displays a strong sensitivity of the random dynamic amplification with respect to uncertainties.  ... 
doi:10.1016/j.jsv.2015.07.006 fatcat:z3eulimh4veijpdlvpfgkncln4

Threshold-Controlled Global Cascading in Wireless Sensor Networks [article]

Qiming Lu, Gyorgy Korniss, Boleslaw K. Szymanski
2006 arXiv   pre-print
We investigate cascade dynamics in threshold-controlled (multiplex) propagation on random geometric networks.  ...  We also consider the same dynamics on a modified network by adding a few long-range communication links, resulting in a small-world network.  ...  ACKNOWLEDGMENT We thank Zoltán Toroczkai and Hasan Guclu for discussions and sharing some of his (H.G.) earlier codes generating random geometric networks.  ... 
arXiv:cs/0606054v1 fatcat:kczm6v2hdrdpfb2bc6la6zoobi

GEOMETRIC EVOLUTIONARY DYNAMICS OF PROTEIN INTERACTION NETWORKS [chapter]

NATAŠA PRŽULJ, OLEKSII KUCHAIEV, ALEKSANDAR STEVANOVIĆ, WAYNE HAYES
2009 Biocomputing 2010  
The model integrates geometric network properties with evolutionary dynamics of PPI network evolution.  ...  Many different network models have been proposed, from those that follow powerlaw degree distributions and those that model complementarity of protein binding domains, to those that have geometric properties  ...  For a geometric network-driven model, see . 11 Geometric Gene Duplication and Mutation Models A geometric random graph 28 is a graph G(V, E) with the set of nodes V distributed uniformly at random in  ... 
doi:10.1142/9789814295291_0020 fatcat:zkmhln3wuvbzvl3i2lngllfbfm

Information Spreading in Stationary Markovian Evolving Graphs [article]

Andrea Clementi, Angelo Monti, Francesco Pasquale, Riccardo Silvestri
2011 arXiv   pre-print
"Geometric Markovian evolving graphs" where the Markovian behaviour is yielded by "n" mobile radio stations, with fixed transmission radius, that perform independent random walks over a square region of  ...  We apply our theorem in two natural and relevant cases of such dynamic graphs.  ...  Observe that setting q = 1 − p yields (time-independent) dynamic random graphs studied in [10] to model dynamic radio networks and in [5] to model epidemic biological processes; here links, at every  ... 
arXiv:1103.0741v1 fatcat:ymff75knmfdyljxj3psikypab4

GOPHER: Categorical probabilistic forecasting with graph structure via local continuous-time dynamics [article]

Ke Alexander Wang, Danielle Maddix, Yuyang Wang
2021 arXiv   pre-print
We consider the problem of probabilistic forecasting over categories with graph structure, where the dynamics at a vertex depends on its local connectivity structure.  ...  We present GOPHER, a method that combines the inductive bias of graph neural networks with neural ODEs to capture the intrinsic local continuous-time dynamics of our probabilistic forecasts.  ...  We generate the geometric graph dataset by generating a random geometric graph via the networkx python package and drawing a random sample of {A uv }.  ... 
arXiv:2112.09964v1 fatcat:tshojwojaffordbwpaluoaail4

Robust Loop Closure Detection Integrating Visual–Spatial–Semantic Information via Topological Graphs and CNN Features

Yuwei Wang, Yuanying Qiu, Peitao Cheng, Xuechao Duan
2020 Remote Sensing  
Firstly, to reduce mismatches under different viewpoints, semantic topological graphs are introduced to encode the spatial relationships of landmarks, and random walk descriptors are employed to characterize  ...  the topological graphs for graph matching.  ...  Thus, the random walk graph descriptor proposed in Section 2.1.4 was used to calculate geometric similarity for graph matching.  ... 
doi:10.3390/rs12233890 fatcat:mjlzmdsoqbak7f5aq6rhheqoqi
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