Networks

 
 
Oxford University Press
  • 2. Auflage
  • |
  • erschienen am 4. Juli 2018
  • |
  • 784 Seiten
 
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-0-19-252749-3 (ISBN)
 
The study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on an unprecedented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.
2. Auflage
  • Englisch
  • Oxford
  • |
  • Großbritannien
161 figures/illustrations
  • 25,66 MB
978-0-19-252749-3 (9780192527493)
weitere Ausgaben werden ermittelt
Mark Newman received a D.Phil. in physics from the University of Oxford in 1991 and conducted postdoctoral research at Cornell University before joining the staff of the Santa Fe Institute, a think-tank in New Mexico devoted to the study of complex systems. In 2002 he left Santa Fe for the University of Michigan, where he is currently Anatol Rapoport Distinguished University Professor of Physics and a professor in the university's Center for the Study of Complex Systems.
  • Cover
  • Networks
  • Copyright
  • Contents
  • Preface
  • Chapter 1. Introduction
  • Examples of networks
  • What can we learn from networks?
  • Properties of networks
  • Outline of this book
  • Part I. The Empirical study of networks
  • Chapter 2. Technological networks
  • 2.1 The Internet
  • 2.1.1 Measuring Internet structure using traceroute
  • 2.1.2 Measuring Internet structure using routing tables
  • 2.2 The telephone network
  • 2.3 Power grids
  • 2.4 Transportation networks
  • 2.5 Delivery and distribution networks
  • Chapter 3. Networks of information
  • 3.1 The World Wide Web
  • 3.2 Citation networks
  • 3.2.1 Patent and legal citations
  • 3.3 Other information networks
  • 3.3.1 Peer-to-peer networks
  • 3.3.2 Recommender networks
  • 3.3.3 Keyword indexes
  • Chapter 4. Social networks
  • 4.1 The empirical study of social networks
  • 4.2 Interviews and questionnaires
  • 4.2.1 Ego-centered networks
  • 4.3 Direct observation
  • 4.4 Data from archival or third-party records
  • 4.5 Affiliation networks
  • 4.6 The small-world experiment
  • 4.7 Snowball sampling, contact tracing, and random walks
  • Chapter 5. Biological networks
  • 5.1 Biochemical networks
  • 5.1.1 Metabolic networks
  • 5.1.2 Protein-protein interaction networks
  • 5.1.3 Genetic regulatory networks
  • 5.1.4 Other biochemical networks
  • 5.2 Networks in the brain
  • 5.2.1 Networks of neurons
  • 5.2.2 Networks of functional connectivity in the brain
  • 5.3 Ecological networks
  • 5.3.1 Food webs
  • 5.3.2 Other ecological networks
  • Part II. Fundamentals of network theory
  • Chapter 6. Mathematics of networks
  • 6.1 Networks and their representation
  • 6.2 The adjacency matrix
  • 6.3 Weighted networks
  • 6.4 Directed networks
  • 6.4.1 Acyclic networks
  • 6.5 Hypergraphs
  • 6.6 Bipartite networks
  • 6.6.1 The incidence matrix and network projections
  • 6.7 Multilayer and dynamic networks
  • 6.8 Trees
  • 6.9 Planar networks
  • 6.10 Degree
  • 6.10.1 Density and sparsity
  • 6.10.2 Directed networks
  • 6.11 Walks and paths
  • 6.11.1 Shortest paths
  • 6.12 Components
  • 6.12.1 Components in directed networks
  • 6.13 Independent paths, connectivity, and cut sets
  • 6.13.1 Maximum flows and cut sets on weighted networks
  • 6.14 The graph Laplacian
  • 6.14.1 Graph partitioning
  • 6.14.2 Network visualization
  • 6.14.3 Random walks
  • 6.14.4 Resistor networks
  • 6.14.5 Properties of the graph Laplacian
  • Exercises
  • Chapter 7. Measures and metrics
  • 7.1 Centrality
  • 7.1.1 Degree centrality
  • 7.1.2 Eigenvector centrality
  • 7.1.3 Katz centrality
  • 7.1.4 PageRank
  • 7.1.5 Hubs and authorities
  • 7.1.6 Closeness centrality
  • 7.1.7 Betweenness centrality
  • 7.2 Groups of nodes
  • 7.2.1 Cliques
  • 7.2.2 Cores
  • 7.2.3 Components and k-components
  • 7.3 Transitivity and the clustering coefficient
  • 7.3.1 Local clustering and redundancy
  • 7.4 Reciprocity
  • 7.5 Signed edges and structural balance
  • 7.6 Similarity
  • 7.6.1 Measures of structural equivalence
  • 7.6.2 Measures of regular equivalence
  • 7.7 Homophily and assortative mixing
  • 7.7.1 Assortative mixing by unordered characteristics
  • 7.7.2 Assortative mixing by ordered characteristics
  • 7.7.3 Assortative mixing by degree
  • Exercises
  • Chapter 8. Computer algorithms
  • 8.1 Software for network analysis and visualization
  • 8.2 Running time and computational complexity
  • 8.3 Storing network data
  • 8.3.1 The adjacency matrix
  • 8.3.2 The adjacency list
  • 8.3.3 Other network representations
  • 8.4 Algorithms for basic network quantities
  • 8.4.1 Degrees
  • 8.4.2 Clustering coefficients
  • 8.5 Shortest paths and breadth-first search
  • 8.5.1 Description of the breadth-first search algorithm
  • 8.5.2 A naive implementation
  • 8.5.3 A better implementation
  • 8.5.4 Variants of breadth-first search
  • 8.5.5 Finding shortest paths
  • 8.5.6 Betweenness centrality
  • 8.6 Shortest paths in networks with varying edge lengths
  • 8.7 Maximum flows and minimum cuts
  • 8.7.1 The augmenting path algorithm
  • 8.7.2 Implementation and running time
  • 8.7.3 Why the algorithm gives correct answers
  • 8.7.4 Finding independent paths and minimum cut sets
  • 8.7.5 Node-independent paths
  • Exercises
  • Chapter 9. Network statistics and measurement error
  • 9.1 Types of error
  • 9.2 Sources of error
  • 9.3 Estimating errors
  • 9.3.1 Conventional statistics of measurement error
  • 9.3.2 The method of maximum likelihood
  • 9.3.3 Errors in network data
  • 9.3.4 The EM algorithm
  • 9.3.5 Independent edge errors
  • 9.3.6 Example
  • 9.3.7 Estimation of other quantities
  • 9.3.8 Other error models
  • 9.4 Correcting errors
  • 9.4.1 Link prediction
  • 9.4.2 Node disambiguation
  • Exercises
  • Chapter 10. The structure of real-world networks
  • 10.1 Components
  • 10.1.1 Components in directed networks
  • 10.2 Shortest paths and the small-world effect
  • 10.3 Degree distributions
  • 10.4 Power laws and scale-free networks
  • 10.4.1 Detecting and visualizing power laws
  • 10.4.2 Properties of power-law distributions
  • 10.5 Distributions of other centrality measures
  • 10.6 Clustering coefficients
  • 10.6.1 Local clustering coefficient
  • 10.7 Assortative mixing
  • Exercises
  • Part III. Network models
  • Chapter 11. Random graphs
  • 11.1 Random graphs
  • 11.2 Mean number of edges and mean degree
  • 11.3 Degree distribution
  • 11.4 Clustering coefficient
  • 11.5 Giant component
  • 11.5.1 Can there be more than one giant component?
  • 11.6 Small components
  • 11.7 Path lengths
  • 11.8 Problems with the random graph
  • Exercises
  • Chapter 12. The configuration model
  • 12.1 The configuration model
  • 12.1.1 Edge probability in the configuration model
  • 12.1.2 Random graphs with given expected degree
  • 12.2 Excess degree distribution
  • 12.3 Clustering coefficient
  • 12.4 Locally tree-like networks
  • 12.5 Number of second neighbors of a node
  • 12.6 Giant component
  • 12.6.1 Example
  • 12.6.2 General solution for the size of the giant component
  • 12.7 Small components
  • 12.7.1 Degrees of nodes in the small components
  • 12.7.2 Average number of nodes reached along an edge
  • 12.8 Networks with power-law degree distributions
  • 12.9 Diameter
  • 12.10 Generating function methods
  • 12.10.1 Generating functions
  • 12.10.2 Examples
  • 12.10.3 Power-law distributions
  • 12.10.4 Normalization and moments
  • 12.10.5 Products of generating functions
  • 12.10.6 Generating functions for degree distributions
  • 12.10.7 Number of second neighbors of a node
  • 12.10.8 Generating functions for the small components
  • 12.10.9 Complete distribution of small component sizes
  • 12.11 Other random graph models
  • 12.11.1 Directed networks
  • 12.11.2 Bipartite networks
  • 12.11.3 Acyclic networks
  • 12.11.4 Degree correlations
  • 12.11.5 Clustering and transitivity
  • 12.11.6 Assortative mixing and community structure
  • 12.11.7 Dynamic networks
  • 12.11.8 The small-world model
  • Exercises
  • Chapter 13. Models of network formation
  • 13.1 Preferential attachment
  • 13.1.1 Degree distribution of Price's model
  • 13.1.2 Computer simulation of Price's model
  • 13.2 The model of Barabasi and Albert
  • 13.3 Time evolution of the network and the first mover effect
  • 13.4 Extensions of preferential attachment models
  • 13.4.1 Addition of extra edges
  • 13.4.2 Removal of edges
  • 13.4.3 Non-linear preferential attachment
  • 13.5 Node copying models
  • 13.6 Network optimization models
  • 13.6.1 Trade-offs between travel time and cost
  • Exercises
  • Part IV. Applications
  • Chapter 14. Community structure
  • 14.1 Dividing networks into groups
  • 14.2 Modularity maximization
  • 14.2.1 The form of the modularity function
  • 14.2.2 A simple modularity maximization algorithm
  • 14.2.3 Spectral modularity maximization
  • 14.2.4 Division into more than two groups
  • 14.2.5 The Louvain algorithm
  • 14.2.6 Resolution limit for modularity maximization
  • 14.3 Methods based on information theory
  • 14.4 Methods based on statistical inference
  • 14.4.1 Community detection using statistical inference
  • 14.5 Other algorithms for community detection
  • 14.5.1 Betweenness-based methods
  • 14.5.2 Hierarchical clustering
  • 14.6 Measuring algorithm performance
  • 14.6.1 Tests on real-world networks
  • 14.6.2 Artificial test networks
  • 14.6.3 Quantifying performance
  • 14.6.4 Comparison of community detection algorithms
  • 14.7 Detecting other kinds of network structure
  • 14.7.1 Overlapping communities
  • 14.7.2 Hierarchical communities
  • 14.7.3 Core-periphery structure
  • 14.7.4 Latent spaces, stratified networks, and rank structure
  • Exercises
  • Chapter 15. Percolation and network resilience
  • 15.1 Percolation
  • 15.2 Uniform random removal of nodes
  • 15.2.1 Uniform removal in the configuration model
  • 15.3 Non-uniform removal of nodes
  • 15.4 Percolation in real-world networks
  • 15.5 Computer algorithms for percolation
  • 15.5.1 Results for real-world networks
  • Exercises
  • Chapter 16. Epidemics on networks
  • 16.1 Models of the spread of infection
  • 16.1.1 The SI model
  • 16.1.2 The SIR model
  • 16.1.3 Solution of the SIR model
  • 16.1.4 Basic reproduction number
  • 16.1.5 The SIS model
  • 16.1.6 The SIRS model
  • 16.1.7 Other epidemic models
  • 16.1.8 Combinations of diseases
  • 16.1.9 Complex contagion and the spread of information
  • 16.2 Epidemic models on networks
  • 16.3 Outbreak sizes and percolation
  • 16.3.1 Outbreak sizes in the SIR model
  • 16.3.2 SIR model and the configuration model
  • 16.3.3 Coexisting diseases
  • 16.3.4 Coinfection
  • 16.3.5 Complex contagion
  • 16.4 Time-dependent properties of epidemics on networks
  • 16.5 Time-dependent properties of the SI model
  • 16.5.1 Pair approximation
  • 16.5.2 Degree-based approximation for the SI model
  • 16.6 Time-dependent properties of the SIR model
  • 16.6.1 Degree-based approximation for the SIR model
  • 16.7 Time-dependent properties of the SIS model
  • 16.7.1 Degree-based approximation for the SIS model
  • Exercises
  • Chapter 17. Dynamical systems on networks
  • 17.1 Dynamical systems
  • 17.1.1 Fixed points and linearization
  • 17.2 Dynamics on networks
  • 17.2.1 Linear stability analysis
  • 17.2.2 Special cases
  • 17.2.3 An example
  • 17.3 Dynamics with more than one variable per node
  • 17.3.1 Special cases
  • 17.4 Spectra of networks
  • 17.5 Synchronization
  • Exercises
  • Chapter 18. Network search
  • 18.1 Web search
  • 18.2 Searching distributed databases
  • 18.3 Sending messages
  • 18.3.1 Kleinberg's model
  • 18.3.2 A hierarchical model for messages
  • Exercises
  • References
  • Index

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