Google matrix analysis of directed networks
arXiv:1409.0428 · doi:10.1103/RevModPhys.87.1261
Abstract
In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social and communication networks, new mathematical methods have been invented to characterize the properties of these networks on a more detailed and precise level. Various search engines are essentially using such methods. It is highly important to develop new tools to classify and rank enormous amount of network information in a way adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency on various examples including World Wide Web, Wikipedia, software architecture, world trade, social and citation networks, brain neural networks, DNA sequences and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos and Random Matrix theory.
56 pages, 58 figures. Missed link added in network example of Fig3a
References in corpus (69)
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Community detection in graphs
- The structure of scientific collaboration networks
- Statistical physics of social dynamics
- Critical phenomena in complex networks
- Random Matrix Theories in Quantum Physics: Common Concepts
- Anderson Transitions
- How Popular is Your Paper? An Empirical Study of the Citation Distribution
- Self-similarity of complex networks
- Topology of evolving networks: local events and universality
- Opinion evolution in closed community
- Structure and Evolution of the World Trade Network
- Sociophysics: A review of Galam models
- Citation Statistics from 110 Years of Physical Review
- Why Nestedness in Mutualistic Networks?
- Diffusion of scientific credits and the ranking of scientists
- Preferential attachment in the growth of social networks: the case of Wikipedia
- Multinetwork of international trade: A commodity-specific analysis
- Ruelle-Perron-Frobenius spectrum for Anosov maps
- Wikipedias: Collaborative web-based encyclopedias as complex networks
- Distribution of Eigenvalues in Non-Hermitian Anderson Model
- Patterns of dominant flows in the world trade web
- Fractal Weyl laws for chaotic open systems
- Structure and Response in the World Trade Network
- Two-dimensional ranking of Wikipedia articles
- Random unistochastic matrices
- Interactions of cultures and top people of Wikipedia from ranking of 24 language editions
- Fractal Weyl law for quantum fractal eigenstates
- Towards physical laws for software architecture
- Quantum computing of delocalization in small-world networks
- PageRank model of opinion formation on social networks
- Spectral properties of the Google matrix of the World Wide Web and other directed networks
- Distribution of resonances for open quantum maps
- Ulam method and fractal Weyl law for Perron--Frobenius operators
- Ulam method for the Chirikov standard map
- Opinion formation driven by PageRank node influence on directed networks
- Delocalization transition for the Google matrix
- Quantum Chaos & Quantum Computers
- Google matrix analysis of the multiproduct world trade network
- Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles
- Two classes of bipartite networks: nested biological and social systems
- Google matrix, dynamical attractors and Ulam networks
- Ecological analysis of world trade
- Spectral properties of Google matrix of Wikipedia and other networks
- Schroedinger-like PageRank equation and localization in the WWW
- Towards two-dimensional search engines
- Time evolution of Wikipedia network ranking
- Google matrix and Ulam networks of intermittency maps
- Universality of spectra for interacting quantum chaotic systems
- Universal Emergence of PageRank
- Google matrix of Twitter
- Diffusion and localization for the Chirikov typical map
- Towards Google matrix of brain
- Poincaré recurrences and Ulam method for the Chirikov standard map
- Fractal Weyl law for Linux Kernel Architecture
- Google matrix of the world network of economic activities
- Poincaré recurrences of DNA sequence
- PageRank of integers
- Google matrix of the citation network of Physical Review
- Biographical Social Networks on Wikipedia - A cross-cultural study of links that made history
- The game of go as a complex network
- Google matrix analysis of DNA sequences
- PageRank model of opinion formation on Ulam networks
- Google matrix of business process management
- Move ordering and communities in complex networks describing the game of go
- Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks
- Google matrix analysis of C.elegans neural network
- Anderson transition for Google matrix eigenstates
Cited by in corpus (63)
- Vital nodes identification in complex networks
- Complex network approaches to nonlinear time series analysis
- Ranking in evolving complex networks
- Mapping multiplex hubs in human functional brain network
- Random walks on networks with stochastic resetting
- Identification of milestone papers through time-balanced network centrality
- Spectral Theory of Sparse Non-Hermitian Random Matrices
- Quantifying and suppressing ranking bias in a large citation network
- Diffusive transport on networks with stochastic resetting to multiple nodes
- Wikipedia mining of hidden links between political leaders
- Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure
- Wikipedia Ranking of World Universities
- Network structural origin of instabilities in large complex systems
- Random walks on complex networks with first-passage resetting
- Linear stability analysis for large dynamical systems on directed random graphs
- Resonances for open quantum maps and a fractal uncertainty principle
- World influence and interactions of universities from Wikipedia networks
- The mathematics of non-linear metrics for nested networks
- Random walks on complex networks under node-dependent stochastic resetting
- Optimized evolution of networks for principal eigenvector localization
- Random walks on complex networks under time-dependent stochastic resetting
- Influence of petroleum and gas trade on EU economies from the reduced Google matrix analysis of UN COMTRADE data
- Eigenvalue Repulsion and Eigenfunction Localization in Sparse Non-Hermitian Random Matrices
- Ising-PageRank model of opinion formation on social networks
- Nonlocal biased random walks and fractional transport on directed networks
- Mean encounter times for multiple random walkers on networks
- Crisis contagion in the world trade network
- Prospects of BRICS currency dominance in international trade
- Random walks on complex networks with multiple resetting nodes: a renewal approach
- Google matrix of Bitcoin network
- COVID-19 impact on the international trade
- Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
- Capturing the influence of geopolitical ties from Wikipedia with reduced Google matrix
- Small world of Ulam networks for chaotic Hamiltonian dynamics
- Interactions and influence of world painters from the reduced Google matrix of Wikipedia networks
- Correspondence behavior of classical and quantum dissipative directed transport via thermal noise
- Multi-cultural Wikipedia mining of geopolitics interactions leveraging reduced Google matrix analysis
- Analysis of world terror networks from the reduced Google matrix of Wikipedia
- Google matrix analysis of bi-functional SIGNOR network of protein-protein interactions
- From Spectra to Localized Networks: A Reverse Engineering Approach
- Optimal exploration of random walks with local bias on networks
- Evolution of transport under cumulative damage in metro systems
- World impact of kernel European Union 9 countries from Google matrix analysis of the world trade network
- Centralities in complex networks
- Interdependence of sectors of economic activities for world countries from the reduced Google matrix analysis of WTO data
- What is the central bank of Wikipedia?
- Chaos simplifies quantum friction
- 3D classical and quantum stable structures of dissipative systems
- Opinion formation in the world trade network
- Classical to quantum correspondence in dissipative directed transport
- Contagion in Bitcoin networks
- A spin glass approach to the directed feedback vertex set problem
- Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole
- Mathematical Study of Scattering Resonances
- Classical properties of the leading eigenstates of quantum dissipative systems
- Abrupt transitions in the optimization of diffusion with distributed resetting
- Large-scale Sustainable Search on Unconventional Computing Hardware
- Post-Brexit power of European Union from the world trade network analysis
- Harmonic structures of Beethoven quartets: a complex network approach
- Non-equilibrium random walks on multiplex networks
- Confrontation of capitalism and socialism in Wikipedia networks
- Relations of society concepts and religions from Wikipedia networks
- Robust Temporal Ensembling for Learning with Noisy Labels