Random Geometric Graphs

Abstract

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. 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. Insights relevant for graph bi-partitioning are included.

16 pages, 10 figures. Minor changes. Added references

References in corpus (5)

• Statistical mechanics of complex networks
• Clustering and preferential attachment in growing networks
• Are randomly grown graphs really random?
• Extremal Optimization for Graph Partitioning
• Random walks on fractals and stretched exponential relaxation

Cited by in corpus (178)

• Spatial Networks
• Complex network approaches to nonlinear time series analysis
• Recurrence networks - A novel paradigm for nonlinear time series analysis
• The spatial structure of networks
• The physics of brain network structure, function, and control
• Generative models of the human connectome
• Fundamental structures of dynamic social networks
• Effects of mobility in a population of Prisoner's Dilemma players
• Crossover from Scale-Free to Spatial Networks
• Network Geometry
• Synchronization in networks of mobile oscillators
• The synchronized dynamics of time-varying networks
• The Geometry of Chaotic Dynamics -- A Complex Network Perspective
• Majority-vote model on random graphs
• Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
• Ambiguities in recurrence-based complex network representations of time series
• The Influence of Network Topology on Sound Propagation in Granular Materials
• Analytical framework for recurrence-network analysis of time series
• The Naming Game in Social Networks: Community Formation and Consensus Engineering
• Opinion Polarization by Learning from Social Feedback
• Resolving structural variability in network models and the brain
• Disentangling different types of El Niño episodes by evolving climate network analysis
• WiFi Epidemiology: Can Your Neighbors' Router Make Yours Sick?
• On the Secure and Reconfigurable Multi-Layer Network Design for Critical Information Dissemination in the Internet of Battlefield Things (IoBT)
• Connectivity Distribution of Spatial Networks
• Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods
• Subgraphs and network motifs in geometric networks
• Worm Epidemics in Wireless Adhoc Networks
• Distributing Multipartite Entanglement over Noisy Quantum Networks
• Naming Games in Two-Dimensional and Small-World-Connected Random Geometric Networks
• Emergence of synchronization in multiplex networks of mobile Rössler oscillators
• Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework
• Master stability functions reveal diffusion-driven pattern formation in networks
• Consensus in networks of mobile communicating agents
• Statistical properties of the quantum internet
• Coevolution of synchronization and cooperation in costly networked interactions
• Degree Correlations in Random Geometric Graphs
• Complex network view of evolving manifolds
• Tuning synchronization of integrate-and-fire oscillators through mobility
• Centrality scaling in large networks
• The topology of large Open Connectome networks for the human brain
• Geographical effects on cascading breakdowns of scale-free networks
• Network comparison and the within-ensemble graph distance
• Diffusive transport on networks with stochastic resetting to multiple nodes
• Synchronization in dynamical networks of locally coupled self-propelled oscillators
• Topological data analysis of continuum percolation with disks
• Robustness of Noisy Quantum Networks
• Crossovers in ScaleFree Networks on Geographical Space
• Cascading failures in spatially-embedded random networks
• Random Rectangular Graphs
• Small worlds and clustering in spatial networks
• Networks based on collisions among mobile agents
• Epidemic Spreading in Random Rectangular Networks
• Detecting the ultra low dimensionality of real networks
• Synchronization in Random Geometric Graphs
• Competing Effects of Social Balance and Influence
• Ollivier-Ricci curvature convergence in random geometric graphs
• Predicting epidemic outbreak from individual features of the spreaders
• Is the brain relativistic?
• Homophily as a Process Generating Social Networks: Insights from Social Distance Attachment Model
• Spreading dynamics on spatially constrained complex brain networks
• Secure and Reconfigurable Network Design for Critical Information Dissemination in the Internet of Battlefield Things (IoBT)
• Embedding Graphs in Lorentzian Spacetime
• Finding Patient Zero: Learning Contagion Source with Graph Neural Networks
• Distributive routing & congestion control in wireless multihop ad hoc communication networks
• Self-Assembly of Geometric Space from Random Graphs
• Reconstructing directed and weighted topologies of phase-locked oscillator networks
• Constraining Cosmology with Big Data Statistics of Cosmological Graphs
• Coherent force chains in disordered granular materials emerge from a percolation of quasilinear clusters
• Growing networks under geographical constraints
• Topological versus spectral properties of random geometric graphs
• Optimal transport on wireless networks
• Particle velocity controls phase transitions in contagion dynamics
• Opinion Dynamics and Influencing on Random Geometric Graphs
• Evolution of Cooperation on Spatially Embedded Networks
• Spatially disordered environments stabilize competitive metacommunities
• Detecting hyperbolic geometry in networks: why triangles are not enough
• Scale-free networks embedded in fractal space
• Network Discovery by Generalized Random Walks
• Social distancing in pedestrian dynamics and its effect on disease spreading
• Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows
• Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls
• Epidemic processes on self-propelled particles: continuum and agent-based modelling
• Adaptive Differentially Quantized Subspace Perturbation (ADQSP): A Unified Framework for Privacy-Preserving Distributed Average Consensus
• Connecting Network Science and Information Theory
• The impact of constrained rewiring on network structure and node dynamics
• Enhancing Robustness and Immunization in geographical networks
• Random geometric graph description of connectedness percolation in rod systems
• Scale-invariant geometric random graphs
• Degree difference: A simple measure to characterize structural heterogeneity in complex networks
• Normalized Sombor indices as complexity measures of random graphs
• Concentric Network Symmetry
• Normalised Degree Variance
• Random geometric graphs in high dimension
• Random spherical graphs
• The Gradient Mechanism in a Communication Network
• Synchronization of moving integrate and fire oscillators
• Moving the epidemic tipping point through topologically targeted social distancing
• Can recurrence networks show small world property?
• On neighbourhood degree sequences of complex networks
• Analytical calculation of neighborhood order probabilities for high dimensional Poissonic processes and mean field models
• Comfort-driven mobility produces spatial fragmentation in Axelrod's model
• Statistical mechanics of random geometric graphs: Geometry-induced first order phase transition
• Privacy-Preserving Distributed Expectation Maximization for Gaussian Mixture Model using Subspace Perturbation
• Centralized versus Decentralized Infrastructure Networks
• Directed Random Geometric Graphs
• Transitions in spatial networks
• Complex systems: features, similarity and connectivity
• A Graphical Representation of Membrane Filtration
• An embedding-based distance for temporal graphs
• Naming Games in Spatially-Embedded Random Networks
• A Latent Parameter Node-Centric Model for Spatial Networks
• Evaluating transport in irregular pore networks
• Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization
• Topological conditions drive stability in meta-ecosystems
• Levy geometric graphs
• Explaining the emergence of complex networks through log-normal fitness in a Euclidean node similarity space
• Linear embeddings of graphs and graph limits
• Directed Percolation in Wireless Networks with Interference and Noise
• Geometric evolution of complex networks
• Signal Recovery on Graphs: Fundamental Limits of Sampling Strategies
• Grounding force-directed network layouts with latent space models
• Threshold-Controlled Global Cascading in Wireless Sensor Networks
• Tree-ansatz percolation of hard spheres
• Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
• Combinatorial Quantum Gravity: Emergence of Geometric Space from Random Graphs
• Emergent time, cosmological constant and boundary dimension at infinity in combinatorial quantum gravity
• Infection Analysis on Irregular Networks through Graph Signal Processing
• Non-uniform random graphs on the plane: A scaling study
• Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture
• Underwater Optical Wireless Communications, Networking, and Localization: A Survey
• A Random-Line-Graph Approach to Overlapping Line Segments
• Structured interactions as a stabilizing mechanism for competitive ecosystems
• Topological transition in a coupled dynamic in random networks
• Modeling and Performance Analysis of IoT-over-LEO Satellite Systems under Realistic Operational Constraints: A Stochastic Geometry Approach
• Continuum percolation of polydisperse hyperspheres in infinite dimensions
• Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs
• The Atlas for the Aspiring Network Scientist
• Corrected mean-field model for random sequential adsorption on random geometric graphs
• Characterizing spatial point processes by percolation transitions
• On Data-centric Forwarding in Mobile Ad-hoc Networks: Baseline Design and Simulation Analysis
• Self-organized network design by link survivals and shortcuts
• Outage Probability Analysis of Uplink Heterogeneous Non-terrestrial Networks: A Novel Stochastic Geometry Model
• Competition and evolution in restricted space
• Malleability of complex networks
• Topological Network Entanglement as Order Parameter for the Emergence of Geometry
• Diffusive Persistence on Disordered Lattices and Random Networks
• Weighted random--geometric and random--rectangular graphs: Spectral and eigenfunction properties of the adjacency matrix
• Isotropic random geometric networks in two dimensions with a penetrable cavity
• Real-World Networks are Low-Dimensional: Theoretical and Practical Assessment
• Graph-Dynamics correspondence in metallic glass-forming liquids
• Effects of confinement and vaccination on an epidemic outburst: a statistical mechanics approach
• The Impact of Social Attractiveness on Casual Group Formation: Power-Law Group Sizes and Suppressed Percolation
• Non-equilibrium phase transition and cultural drift in the continuous-trait Axelrod model
• Understanding How Network Geometry Influences Diffusion Processes in Complex Networks: A Focus on Cryptocurrency Blockchains and Critical Infrastructure Networks
• High Performance Algorithms for Quantum Gravity and Cosmology
• On the Power of Edge Independent Graph Models
• Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information
• Privacy-Preserving Distributed Processing: Metrics, Bounds, and Algorithms
• Small world is not enough: Criteria for network choice and conclusiveness of simulations
• Active Sampling for Approximately Bandlimited Graph Signals
• Approximate conditional distributions of distances between nodes in a two-dimensional sensor network
• Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs
• Computing distances on Riemann surfaces
• An Independent Process Approximation to Sparse Random Graphs with a Prescribed Number of Edges and Triangles
• Modelling Diffusion through Statistical Network Analysis: A Simulation Study
• Performance Analysis of Connectivity and Localization in Multi-Hop Underwater Optical Wireless Sensor Networks
• Asymptotic Analysis for Greedy Initialization of Threshold-Based Distributed Optimization of Persistent Monitoring on Graphs
• Uniform {\varepsilon}-Stability of Distributed Nonlinear Filtering over DNAs: Gaussian-Finite HMMs
• Random Spatial Networks: Small Worlds without Clustering, Traveling Waves, and Hop-and-Spread Disease Dynamics
• Spatiotemporal Activity-Driven Networks
• Spectral properties of adjacency and distance matrices for various networks
• On the Analysis of Adaptive-Rate Applications in Data-Centric Wireless Ad-Hoc Networks
• Scalable Sparse Subspace Clustering via Ordered Weighted ${\ell }_1$ Regression
• On the distribution of topological and spectral indices on random graphs
• Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks
• Modeling the Perspectives for Scientific Advancement
• When the spatial networks split?