Sustaining the Internet with Hyperbolic Mapping

Abstract

The Internet infrastructure is severely stressed. Rapidly growing overheads associated with the primary function of the Internet---routing information packets between any two computers in the world---cause concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade. Here we present a method to map the Internet to a hyperbolic space. Guided with the constructed map, which we release with this paper, Internet routing exhibits scaling properties close to theoretically best possible, thus resolving serious scaling limitations that the Internet faces today. Besides this immediate practical viability, our network mapping method can provide a different perspective on the community structure in complex networks.

References in corpus (11)

• Community structure in social and biological networks
• Modularity and community structure in networks
• Error and attack tolerance of complex networks
• Lethality and centrality in protein networks
• Navigability of Complex Networks
• Self-similarity of complex networks and hidden metric spaces
• Assessing the relevance of node features for network structure
• Traffic-driven Epidemic Spreading in Finite-size Scale-Free Networks
• Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces
• Curvature and temperature of complex networks
• Euclidean versus hyperbolic congestion in idealized versus experimental networks

Cited by in corpus (142)

• Spatial Networks
• Hyperbolic Geometry of Complex Networks
• Popularity versus Similarity in Growing Networks
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Community structure and scale-free collections of Erdös-Rényi graphs
• Network resilience
• Topological strata of weighted complex networks
• Network Geometry
• Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space
• Poincaré Embeddings for Learning Hierarchical Representations
• Emergent Hyperbolic Network Geometry
• Network Mapping by Replaying Hyperbolic Growth
• Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit
• Topological data analysis of contagion maps for examining spreading processes on networks
• Network geometry with flavor: from complexity to quantum geometry
• Hidden geometric correlations in real multiplex networks
• A Survey on Centrality Metrics and Their Implications in Network Resilience
• Multiscale unfolding of real networks by geometric renormalization
• Network Cosmology
• Interdisciplinary and physics challenges of Network Theory
• Topological hyperbolic lattices
• Emergent Complex Network Geometry
• Emergence of Soft Communities from Geometric Preferential Attachment
• Correlation dimension of complex networks
• A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities
• Geometric renormalization unravels self-similarity of the multiscale human connectome
• The hidden geometry of weighted complex networks
• Network Geometry Inference using Common Neighbors
• Clustering implies geometry in networks
• An Experimental Investigation of Hyperbolic Routing with a Smart Forwarding Plane in NDN
• Navigable Networks as Nash Equilibria of Navigation Games
• Statistical inference of assortative community structures
• Synchronization in Network Geometries with Finite Spectral Dimension
• Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models
• Deciphering the global organization of clustering in real complex networks
• Topological implications of negative curvature for biological and social networks
• Principled approach to the selection of the embedding dimension of networks
• Navigable maps of structural brain networks across species
• Complex Quantum Network Geometries: Evolution and Phase Transitions
• Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks
• Topological Percolation on Hyperbolic Simplicial Complexes
• Neural Embeddings of Graphs in Hyperbolic Space
• Metric clusters in evolutionary games on scale-free networks
• Hyperbolic Graph Generator
• Characterizing the analogy between hyperbolic embedding and community structure of complex networks
• Network Geometry and Complexity
• Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
• Link prediction with hyperbolic geometry
• Modeling Structure and Resilience of the Dark Network
• Enhancing neural-network performance via assortativity
• Explosion in weighted Hyperbolic Random Graphs and Geometric Inhomogeneous Random Graphs
• Soft communities in similarity space
• Detecting the ultra low dimensionality of real networks
• Navigability evaluation of complex networks by greedy routing efficiency
• Exploring complex networks via topological embedding on surfaces
• Latent geometry of bipartite networks
• The inherent community structure of hyperbolic networks
• The diameter of KPKVB random graphs
• Hidden Variables in Bipartite Networks
• Average Distance in a General Class of Scale-Free Networks with Underlying Geometry
• Diffusion geometry of multiplex and interdependent systems
• Scalable Hyperbolic Recommender Systems
• HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion
• Finding shortest and nearly shortest path nodes in large substantially incomplete networks
• Renormalization group for link percolation on planar hyperbolic manifolds
• Emergence of geometric Turing patterns in complex networks
• Bootstrap percolation on geometric inhomogeneous random graphs
• Network Alignment
• New Phenomena in Large-Scale Internet Traffic
• Crossing on hyperbolic lattices
• Percolation and the effective structure of complex networks
• Random hyperbolic graphs in $d+1$ dimensions
• Collective navigation of complex networks: Participatory greedy routing
• Model-independent methods for embedding directed networks into Euclidean and hyperbolic spaces
• k-core structure of real multiplex networks
• Link persistence and conditional distances in multiplex networks
• Growing hyperbolic networks beyond two dimensions: the generalised popularity-similarity optimisation model
• Optimisation of the coalescent hyperbolic embedding of complex networks
• Visualizing probabilistic models in Minkowski space with intensive symmetrized Kullback-Leibler embedding
• Unitary Entanglement Construction in Hierarchical Networks
• Network Renormalization
• Complex networks as an emerging property of hierarchical preferential attachment
• Finite-size scaling of geometric renormalization flows in complex networks
• Long-Range Correlations and Memory in the Dynamics of Internet Interdomain Routing
• Scale-free network clustering in hyperbolic and other random graphs
• Explosion and distances in scale-free percolation
• Weighted distances in scale-free configuration models
• On the diameter of hyperbolic random graphs
• Emergent entanglement structures and self-similarity in quantum spin chains
• Zoo Guide to Network Embedding
• Fundamental dynamics of popularity-similarity trajectories in real networks
• Spatial search by continuous-time quantum walks on renormalized Internet networks
• Duality between predictability and reconstructability in complex systems
• The contact process on random hyperbolic graphs: metastability and critical exponents
• Multi-layer network approach in modeling epidemics in an urban town
• A Latent Parameter Node-Centric Model for Spatial Networks
• Random graphs and real networks with weak geometric coupling
• The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks
• From Node Embedding To Community Embedding : A Hyperbolic Approach
• Topological estimation of the latent geometry of a complex network
• Greedy routing optimisation in hyperbolic networks
• Model-free hidden geometry of complex networks
• Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
• Hyperbolic Mapping of Human Proximity Networks
• Greedy Routing and the Algorithmic Small-World Phenomenom
• Geometric detection of hierarchical backbones in real networks
• Generalised thresholding of hidden variable network models with scale-free property
• Geometric randomization of real networks with prescribed degree sequence
• Bitcoin Blockchain Dynamics: the Selfish-Mine Strategy in the Presence of Propagation Delay
• Fast generation of complex networks with underlying hyperbolic geometry
• Complex Networks in the Framework of Nonassociative Geometry
• Systematic comparison of graph embedding methods in practical tasks
• Stopping explosion by penalising transmission to hubs in scale-free spatial random graphs
• Community Detection in the Hyperbolic Space
• Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings
• Topology and Geometry of the Third-Party Domains Ecosystem: Measurement and Applications
• Real-World Networks are Low-Dimensional: Theoretical and Practical Assessment
• Dynamics of cold random hyperbolic graphs with link persistence
• Deductive Way of Reasoning about the Internet AS Level Topology
• Symmetry-driven embedding of networks in hyperbolic space
• Non-Uniqueness Phase in Hyperbolic Marked Random Connection Models using the Spherical Transform
• Bipartite Communities
• Holonomy: A Virtual Reality Exploration of Hyperbolic Geometry
• High Performance Algorithms for Quantum Gravity and Cosmology
• HEAT: Hyperbolic Embedding of Attributed Networks
• Random walk with hyperbolic probabilities
• Enumeration of graphs with a heavy-tailed degree sequence
• Localized geometry detection in scale-free random graphs
• Mathematical models for epidemic spreading on complex networks
• Generalization Error Bound for Hyperbolic Ordinal Embedding
• Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes
• Stable Geodesic Update on Hyperbolic Space and its Application to Poincare Embeddings
• Interplay between Network Topology and Dynamics in Neural Systems
• Generating Tree Structures for Hyperbolic Tessellations
• On the hyperbolicity constant of circular-arc graphs
• On the largest component of subcritical random hyperbolic graphs
• Maximal Cliques in Scale-Free Random Graphs
• Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry
• A High-Performance Evolutionary Multiobjective Community Detection Algorithm
• Negatively Curved Graphs
• $({\omega }_1,{\omega }_2)$-temporal random hyperbolic graphs
• Hermitian Symmetric Spaces for Graph Embeddings