Theoretical Computer Science, ISSN 0304-3975, 02/2019, Volume 760, pp. 35 - 54

Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be...

Sampling algorithms | Real-world networks | Clustering coefficient | Random graph models | Hyperbolic random graphs | Compression algorithms | COMPUTER SCIENCE, THEORY & METHODS

Sampling algorithms | Real-world networks | Clustering coefficient | Random graph models | Hyperbolic random graphs | Compression algorithms | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Journal of Complex Networks, ISSN 2051-1310, 02/2018, Volume 6, Issue 1, pp. 95 - 105

Abstract We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are...

Random geometric graph | Motif | Chen-Stein method | Spectrum

Random geometric graph | Motif | Chen-Stein method | Spectrum

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 4/2016, Volume 26, Issue 2, pp. 986 - 1028

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...

Zero | Statistical graphs | Mathematical theorems | Approximation | Cubes | Poisson equation | Mathematical functions | Connected regions | Probabilities | Vertices | Stochastic geometry | Connectivity | Random connection model | Continuum percolation | Isolated points | Random graph | isolated points | connectivity | random connection model | continuum percolation | STATISTICS & PROBABILITY | stochastic geometry | Mathematics - Probability

Zero | Statistical graphs | Mathematical theorems | Approximation | Cubes | Poisson equation | Mathematical functions | Connected regions | Probabilities | Vertices | Stochastic geometry | Connectivity | Random connection model | Continuum percolation | Isolated points | Random graph | isolated points | connectivity | random connection model | continuum percolation | STATISTICS & PROBABILITY | stochastic geometry | Mathematics - Probability

Journal Article

2003, Oxford studies in probability, ISBN 9780198506263, Volume 5, xiii, 330

This book sets out a body of rigorous mathematical theory for finite graphs with nodes placed randomly in Euclidean d-space according to a common probability...

Random graphs

Random graphs

Book

Discrete Applied Mathematics, ISSN 0166-218X, 12/2014, Volume 178, pp. 149 - 152

We study the vertex pursuit game of Cops and Robbers, in which cops try to capture a robber on the vertices of the graph. The minimum number of cops required...

Vertex-pursuit games | Random graphs | Cops and Robbers | COPS | MATHEMATICS, APPLIED

Vertex-pursuit games | Random graphs | Cops and Robbers | COPS | MATHEMATICS, APPLIED

Journal Article

CLASSICAL AND QUANTUM GRAVITY, ISSN 0264-9381, 06/2019, Volume 36, Issue 12, p. 125012

We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a...

Ollivier curvature | Euclidean quantum gravity | QUANTUM SCIENCE & TECHNOLOGY | emergent space | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | random graphs | quantum gravity | discrete geometry | OLLIVIERS RICCI CURVATURE | statistical mechanics | PHYSICS, PARTICLES & FIELDS

Ollivier curvature | Euclidean quantum gravity | QUANTUM SCIENCE & TECHNOLOGY | emergent space | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | random graphs | quantum gravity | discrete geometry | OLLIVIERS RICCI CURVATURE | statistical mechanics | PHYSICS, PARTICLES & FIELDS

Journal Article

Algorithmica, ISSN 0178-4617, 1/2018, Volume 80, Issue 1, pp. 300 - 330

Consider the random geometric graph $$G = G(n,r_n,f)$$ G = G ( n , r n , f ) consisting of n nodes independently distributed in $$S = \left[...

Theory of Computation | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Primary: 60J10 | 91D30 | Mathematics of Computing | 90B15 | Computer Science | 62E10 | 60K35 | Algorithm Analysis and Problem Complexity | Random geometric graphs | Diameter | Stretch property | Secondary: 60C05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PERCOLATION

Theory of Computation | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Primary: 60J10 | 91D30 | Mathematics of Computing | 90B15 | Computer Science | 62E10 | 60K35 | Algorithm Analysis and Problem Complexity | Random geometric graphs | Diameter | Stretch property | Secondary: 60C05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PERCOLATION

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 04/2013, Volume 61, Issue 7, pp. 1644 - 1656

In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and...

Manifolds | Graph Fourier transform | Fourier transforms | Laplace equations | Graphical models | signal processing | Digital signal processing | network science | Markov random fields | graphical models | DIMENSIONALITY REDUCTION | EIGENMAPS | GEOMETRIC DIFFUSIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TUKEY-TYPE ALGORITHMS | STRUCTURE DEFINITION | HARMONIC-ANALYSIS | TRANSFORMS | TOOL | Measurement | Discrete-time systems | Usage | Image processing | Innovations | Signal processing | Graph theory | Pixels

Manifolds | Graph Fourier transform | Fourier transforms | Laplace equations | Graphical models | signal processing | Digital signal processing | network science | Markov random fields | graphical models | DIMENSIONALITY REDUCTION | EIGENMAPS | GEOMETRIC DIFFUSIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TUKEY-TYPE ALGORITHMS | STRUCTURE DEFINITION | HARMONIC-ANALYSIS | TRANSFORMS | TOOL | Measurement | Discrete-time systems | Usage | Image processing | Innovations | Signal processing | Graph theory | Pixels

Journal Article

9.
Full Text
Explosion in weighted hyperbolic random graphs and geometric inhomogeneous random graphs

Stochastic Processes and their Applications, ISSN 0304-4149, 03/2020, Volume 130, Issue 3, pp. 1309 - 1367

In this paper we study weighted distances in scale-free spatial network models: hyperbolic random graphs, geometric inhomogeneous random graphs and scale-free...

Scale-free property | Small world property | First passage percolation | Spatial network models | Hyperbolic random graphs | Typical distances | Statistics and Probability | Modelling and Simulation | Applied Mathematics | MODELS | DISTANCES | STATISTICS & PROBABILITY | 1ST PASSAGE PERCOLATION | Mathematics - Probability

Scale-free property | Small world property | First passage percolation | Spatial network models | Hyperbolic random graphs | Typical distances | Statistics and Probability | Modelling and Simulation | Applied Mathematics | MODELS | DISTANCES | STATISTICS & PROBABILITY | 1ST PASSAGE PERCOLATION | Mathematics - Probability

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 10/2016, Volume 26, Issue 5, pp. 3078 - 3109

A random geometric irrigation graph Γn(rn, ξ) has n vertices identified by n independent uniformly distributed points X1,..., Xn in the unit square [0, 1]2....

Squares | Mathematical theorems | Lexicography | Cardinality | Random walk | Construction engineering | Explosives | Random variables | Binomials | Vertices | Irrigation graph | Random geometric graph | Connectivity | STATISTICS & PROBABILITY | connectivity | irrigation graph | EXPANSION | Probability | Mathematics | Combinatorics | Networking and Internet Architecture | Computer Science | Discrete Mathematics

Squares | Mathematical theorems | Lexicography | Cardinality | Random walk | Construction engineering | Explosives | Random variables | Binomials | Vertices | Irrigation graph | Random geometric graph | Connectivity | STATISTICS & PROBABILITY | connectivity | irrigation graph | EXPANSION | Probability | Mathematics | Combinatorics | Networking and Internet Architecture | Computer Science | Discrete Mathematics

Journal Article

Annals of Applied Probability, ISSN 1050-5164, 08/2018, Volume 28, Issue 4, pp. 2003 - 2062

Given a graph, the popular "modularity" clustering method specifies a partition of the vertex set as the solution of a certain optimization problem. In this...

Perimeter | Gamma convergence | Kelvin’s problem | Scaling limit | Consistency | Shape optimization | Community detection | Random geometric graph | Total variation | Modularity | Optimal transport | INEQUALITIES | shape optimization | LEAST-PERIMETER | APPROXIMATION | scaling limit | optimal transport | STATISTICS & PROBABILITY | GAMMA-CONVERGENCE | NETWORKS | LIMIT | consistency | LAPLACIAN | Kelvin's problem | random geometric graph | perimeter | OPTIMIZATION | PARTITIONS | total variation | community detection

Perimeter | Gamma convergence | Kelvin’s problem | Scaling limit | Consistency | Shape optimization | Community detection | Random geometric graph | Total variation | Modularity | Optimal transport | INEQUALITIES | shape optimization | LEAST-PERIMETER | APPROXIMATION | scaling limit | optimal transport | STATISTICS & PROBABILITY | GAMMA-CONVERGENCE | NETWORKS | LIMIT | consistency | LAPLACIAN | Kelvin's problem | random geometric graph | perimeter | OPTIMIZATION | PARTITIONS | total variation | community detection

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 2/2016, Volume 162, Issue 4, pp. 1068 - 1083

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically...

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Graph theory | Ad hoc networks | Statistical Physics, Dynamical Systems and Complexity | Statistical mechanics | Network science | Physics | Random geometric graphs | Communication theory | PHYSICS, MATHEMATICAL | Fading channels | Analysis

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Graph theory | Ad hoc networks | Statistical Physics, Dynamical Systems and Complexity | Statistical mechanics | Network science | Physics | Random geometric graphs | Communication theory | PHYSICS, MATHEMATICAL | Fading channels | Analysis

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2017, Volume 31, Issue 2, pp. 1328 - 1354

We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G is an element of g(m, r) in [0, root n](2). More precisely, let re...

Pathwidth | Random geometric graphs | Treedepth | Treewidth | MINORS | MATHEMATICS, APPLIED | treedepth | random geometric graphs | PLANE | TREE-DEPTH | pathwidth | treewidth | Grafs, Teoria de | Teoria de grafs | Matemàtiques i estadística | Matemàtica discreta | Graph theory | Àrees temàtiques de la UPC | Probability | Combinatorics | Mathematics

Pathwidth | Random geometric graphs | Treedepth | Treewidth | MINORS | MATHEMATICS, APPLIED | treedepth | random geometric graphs | PLANE | TREE-DEPTH | pathwidth | treewidth | Grafs, Teoria de | Teoria de grafs | Matemàtiques i estadística | Matemàtica discreta | Graph theory | Àrees temàtiques de la UPC | Probability | Combinatorics | Mathematics

Journal Article

The International Journal of Robotics Research, ISSN 0278-3649, 9/2018, Volume 37, Issue 10, pp. 1117 - 1133

Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs)....

asymptotic optimality | motion planning | probabilistic roadmaps | random geometric graphs | sampling-based algorithms | probabilistic completeness | ROBOTICS | QUALITY | NEIGHBORS | DIAMETER | CONNECTIVITY | TREE | EDGE | Motion planning | Tessellation | Euclidean geometry | Barriers | Road construction | Hypercubes | Graphs | Sampling | Optimization

asymptotic optimality | motion planning | probabilistic roadmaps | random geometric graphs | sampling-based algorithms | probabilistic completeness | ROBOTICS | QUALITY | NEIGHBORS | DIAMETER | CONNECTIVITY | TREE | EDGE | Motion planning | Tessellation | Euclidean geometry | Barriers | Road construction | Hypercubes | Graphs | Sampling | Optimization

Journal Article

Random structures & algorithms, ISSN 1042-9832, 2014, Volume 45, Issue 4, pp. 553 - 607

In a Maker-Breaker game on a graph G, Breaker and Maker alternately claim edges of G. Maker wins if, after all edges have been claimed, the graph induced by...

maker-breaker games | random geometric graphs | maker‐breaker games | Maker-breaker games | Random geometric graphs | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | PLANE | POSITIONAL GAMES | Matching | Algorithms | Lists | Mathematical analysis | Games | Graphs | Neighbouring | Constraining

maker-breaker games | random geometric graphs | maker‐breaker games | Maker-breaker games | Random geometric graphs | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | PLANE | POSITIONAL GAMES | Matching | Algorithms | Lists | Mathematical analysis | Games | Graphs | Neighbouring | Constraining

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 217, pp. 427 - 437

We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is...

Coloring | Random geometric graphs | Asymptotic laws | MATHEMATICS, APPLIED | Laws, regulations and rules | Convergence (Social sciences)

Coloring | Random geometric graphs | Asymptotic laws | MATHEMATICS, APPLIED | Laws, regulations and rules | Convergence (Social sciences)

Journal Article

Pattern Recognition Letters, ISSN 0167-8655, 02/2017, Volume 87, pp. 20 - 28

•A novel random structure graph model, called G-E graphs, has been proposed.•We have introduced some matching techniques for G-E graphs.•Experimental results...

Matching | Image representation | Graph models | Image | Random graph | ALGORITHM | SETS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Matching | Image representation | Graph models | Image | Random graph | ALGORITHM | SETS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

18.
Full Text
Corrected mean-field model for random sequential adsorption on random geometric graphs

Journal of Statistical Physics, ISSN 0022-4715, 11/2018, Volume 173, Issue 3-4, pp. 872 - 894

A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the...

Random sequential adsorption | Statistical and Nonlinear Physics | Mathematical Physics | Jamming fraction | Random geometric graph | Functional limit theorems | Mean-field analysis | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics and Dynamical Systems | MODERATE DEVIATIONS | GAUSSIAN LIMITS | PACKING | EPIDEMICS | PHYSICS, MATHEMATICAL | FUNCTIONALS

Random sequential adsorption | Statistical and Nonlinear Physics | Mathematical Physics | Jamming fraction | Random geometric graph | Functional limit theorems | Mean-field analysis | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics and Dynamical Systems | MODERATE DEVIATIONS | GAUSSIAN LIMITS | PACKING | EPIDEMICS | PHYSICS, MATHEMATICAL | FUNCTIONALS

Journal Article

19.
Full Text
Isolation and Connectivity in Random Geometric Graphs with Self-similar Intensity Measures

Journal of Statistical Physics, ISSN 0022-4715, 8/2018, Volume 172, Issue 3, pp. 679 - 700

Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the...

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Random geometric graph | Connectivity | Quantum Physics | Fractals | Physics | Statistical Physics and Dynamical Systems | Degree distribution | MOBILITY MODEL | PERCOLATION | PHYSICS, MATHEMATICAL

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Random geometric graph | Connectivity | Quantum Physics | Fractals | Physics | Statistical Physics and Dynamical Systems | Degree distribution | MOBILITY MODEL | PERCOLATION | PHYSICS, MATHEMATICAL

Journal Article