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Connectivity in Random Annulus Graphs and the Geometric Block Model [article]

Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha
2020 arXiv   pre-print
Our next contribution is in using the connectivity of random annulus graphs to provide necessary and sufficient conditions for efficient recovery of communities for the geometric block model (GBM).  ...  We provide new connectivity results for vertex-random graphs or random annulus graphs which are significant generalizations of random geometric graphs.  ...  Defining a block model over a random geometric graph, the geometric block model (GBM), circumvents this since GBM naturally inherits the transitivity property of a random geometric graph.  ... 
arXiv:1804.05013v3 fatcat:krglqyny7be5havuidaudhqkfm

Connectivity of Random Annulus Graphs and the Geometric Block Model

Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
The geometric block model (GBM) is a probabilistic model for community detection defined over random geometric graphs (RGG) similar in spirit to the popular stochastic block model which is defined over  ...  This requires us to prove new connectivity results for vertex-random graphs or random annulus graphs which are natural generalizations of random geometric graphs.  ...  APPROX/RANDOM 2019 53:10 Connectivity of Random Annulus Graphs and the Geometric Block Model Corollary 13.  ... 
doi:10.4230/lipics.approx-random.2019.53 dblp:conf/approx/GalhotraMPS19 fatcat:tetizrgfbrftbjyuavagtojt2a

Communication-free Massively Distributed Graph Generation [article]

Daniel Funke, Sebastian Lamm, Ulrich Meyer, Peter Sanders, Manuel Penschuck, Christian Schulz, Darren Strash, Moritz von Looz
2019 arXiv   pre-print
In this work, we present novel generators for a variety of network models that are frequently used as benchmarks.  ...  The resulting generators are thus embarrassingly parallel and have a near optimal scaling behavior.  ...  Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF).  ... 
arXiv:1710.07565v3 fatcat:6lplo2xabvf3jd4xedqjrzb64e

Continuum Percolation with Unreliable and Spread-Out Connections

Massimo Franceschetti, Lorna Booth, Matthew Cook, Ronald Meester, Jehoshua Bruck
2005 Journal of statistical physics  
We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models.  ...  We look at two different transformations that spread-out connections and decrease the critical percolation density while preserving the average node degree.  ...  The resulting random graph can now effectively be viewed as a realization of a random connection model with density λ and connection function ph p (x) = g squash p .  ... 
doi:10.1007/s10955-004-8826-0 fatcat:zi2x3qnxmngntebv3qfaauj3qm

Connectivity and Centrality in Dense Random Geometric Graphs [article]

Alexander P. Kartun-Giles
2019 arXiv   pre-print
Our analysis involves a stochastic spatial network model called a random geometric graph, which we use to model a network of interconnected devices communicating wirelessly without any separate, pre-established  ...  [The remaining abstract is available in the front matter of this thesis.]  ...  In Chapter Three we study the effect of non-convexity on the random connection model. In Chapter Four we introduce betweenness centrality in asymptotically dense random geometric graphs.  ... 
arXiv:1601.03296v5 fatcat:vhe2xazplfd43myy2u4elsjkrm

Multi-Dimensional Interval Algebra with Symmetry for Describing Block Layouts [chapter]

Ankur Lahoti, Rohit Singh, Amitabha Mukerjee
2000 Lecture Notes in Computer Science  
Inequalities Quadratic inequalities on a graphing calculator, solutions to systems of quadratic inequalities on a graphing calculator Chapter 1: The Building Blocks of Geometr y: Making and Measuring  ...  Paths in small block diagrams, sums required to solve small block-diagram problems, quickest routes in small block diagrams, estimate of paths in large block diagrams 5.2 Permutations: When Order Counts  ...  Graphs and Tables Chapter 4 The unit circle Display 4.17  ... 
doi:10.1007/3-540-40953-x_12 fatcat:gxyywcuhyffzrce3i7ovomwhuu

Phase transitions and percolation at criticality in enhanced random connection models [article]

Srikanth K. Iyer, Sanjoy Kr. Jhawar
2020 arXiv   pre-print
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick  ...  Intersecting lines form a path in the graph. A graph is said to percolate if there is an infinite connected component or path.  ...  ACKNOWLEDGEMENTS: The authors are thankful to Mathew D. Penrose and Yogeshwaran D. for many useful discussions and references.  ... 
arXiv:1908.00346v3 fatcat:7mannbbivvdzfeiwbmmpzheami

Gromov Centrality: A Multi-Scale Measure of Network Centrality Using Triangle Inequality Excess [article]

Shazia'Ayn Babul, Karel Devriendt, Renaud Lambiotte
2022 arXiv   pre-print
We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and  ...  Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and recovers as limits well-known concept such as the clustering  ...  KD was supported by The Alan Turing Institute under EPSRC grant EP/N510129/1. The work of RL was supported by EPSRC grants EP/V013068/1 and EP/V03474X/1.  ... 
arXiv:2205.04974v1 fatcat:xd4ksq7oxff3jkmn5prkfgvxkq

First Passage Percolation on Random Geometric Graphs and an Application to Shortest-Path Trees

C. Hirsch, D. Neuhäuser, C. Gloaguen, V. Schmidt
2015 Advances in Applied Probability  
We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry  ...  Besides, for a wide class of stationary and isotropic random geometric graphs, our linear growth property implies a shape theorem for the Euclidean first passage model defined by such random geometric  ...  edge set of G Description of the model G = random geometric graph in R 2 as above G * = Palm version of G informally: shifting o to random location on the edge set of G Y λ = Cox process on G * with intensity  ... 
doi:10.1239/aap/1435236978 fatcat:xwno776zqjbe3jp44o7jyv3d54

Bootstrap percolation in random geometric graphs [article]

Victor Falgas-Ravry, Amites Sarkar
2021 arXiv   pre-print
Following Bradonjić and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the 2-dimensional torus.  ...  In this model, the expected number of vertices of the graph is n, and the expected degree of a vertex is alog n for some fixed a>1.  ...  Acknowledgements Research on this project was done while the second author visited the first author in Umeå in Spring 2018 with financial support from STINT Initiation grant IB 2017-7360, which the authors  ... 
arXiv:2110.12166v1 fatcat:ja27g6o2brek5ggj6sku7vu53m

Heat diffusion distance processes: a statistically founded method to analyze graph data sets [article]

Etienne Lasalle
2021 arXiv   pre-print
The statistical properties of empirical means of such processes are studied in the general case.  ...  We propose two multiscale comparisons of graphs using heat diffusion, allowing to compare graphs without node correspondence or even with different sizes.  ...  Acknowledgments I am thankful to Frédéric Chazal 1 and Pascal Massart 2 for the valuable discussions and advice on this work.  ... 
arXiv:2109.13213v2 fatcat:a7o57i2k2zadhdvdowmtgqckey

Exponential rate for the contact process extinction time [article]

Bruno Schapira, Daniel Valesin
2018 arXiv   pre-print
The graphs we treat include various percolation models on increasing boxes of Z d or R d in their supercritical or percolative regimes (Bernoulli bond and site percolation, the occupied and vacant sets  ...  We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models.  ...  We would also like to thank Tobias Müller for helpful discussions and references on the random geometric graph.  ... 
arXiv:1806.04491v1 fatcat:6gx7flrdvbhmdp6duiu2zmt6na

Influence of user density distribution on the pairing probability in GSM cell with implemented VAMOS technology

Dragan Mitić, Aleksandar Lebl, Žarko Markov
2018 Automatika  
It is further presented to what extent the total loss in the system with the implementation of VAMOS technology is greater than the loss in the classic Erlang traffic model with the same traffic characteristics  ...  In this paper, we present the influence of user density distribution in the base station cell on the (un)pairing probability and on the loss caused by the lack of idle traffic resources in GSM systems,  ...  Acknowledgments The paper is written in the framework of projects TR 32051 and TR 32007.  ... 
doi:10.1080/00051144.2018.1502735 fatcat:og6s357cejfixklxrbl4jw6zce

Progressive Correspondence Pruning by Consensus Learning [article]

Chen Zhao, Yixiao Ge, Feng Zhu, Rui Zhao, Hongsheng Li, Mathieu Salzmann
2021 arXiv   pre-print
The selection is challenging since putative matches are typically extremely unbalanced, largely dominated by outliers, and the random distribution of such outliers further complicates the learning process  ...  We introduce a "pruning" block that lets us identify reliable candidates among the initial matches according to consensus scores estimated using local-to-global dynamic graphs.  ...  , and E l i indicates the set of directed edges that connect c i and its neighbors in V l i .  ... 
arXiv:2101.00591v2 fatcat:j7hz2vn6gnezdhauz52j374u3e

Exponential rate for the contact process extinction time

Bruno Schapira, Daniel Valesin
2021 Annales de la Faculté des Sciences de Toulouse  
We would also like to thank Tobias Müller for helpful discussions and references on the random geometric graph.  ...  Acknowledgements We would like to thank Balázs Ráth for directing us to several references on the models we study, leading to a wider applicability of our results.  ...  Random geometric graph The random geometric graph in R d , d 2, is the random graph whose vertex set is a Poisson point process of intensity one, and the edge set is defined with the rule that two vertices  ... 
doi:10.5802/afst.1683 fatcat:gnbgfmf7xjfb7f47xg47so6xdy
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