Statistical Analysis of Network Data Methods and Models

ISBN-10: 038788145X

ISBN-13: 9780387881454

Edition: 2009

Authors: Eric D. Kolaczyk

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Description:

This text provides an up-to-date treatment of the foundations common to the statistical analysis of network data across the disciplines. The material is organized according to a statistical taxonomy, although the presentation entails a conscious balance of concepts versus mathematics.
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Book details

List price: $99.50
Copyright year: 2009
Publisher: Springer London, Limited
Publication date: 3/19/2009
Binding: Hardcover
Pages: 386
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 2.002
Language: English

Introduction and Overview
Why Networks?
Examples of Networks
Technological Networks
Social Networks
Biological Networks
Information Networks
About this Book
Preliminaries
Background on Graphs
Basic Definitions and Concepts
Families of Graphs
Graphs and Matrix Algebra
Graph Data Structures and Algorithms
Background in Probability and Statistics
Probability
Principles of Statistical Inference
Methods of Statistical Inference: Tutorials
Statistical Analysis of Network Data: Prelude
Additional Related Topics and Reading
Exercises
Mapping Networks
Introduction
Collecting Relational Network Data
Measurement of System Elements and Interactions
Enumerated, Partial, and Sampled Data
Constructing Network Graph Representations
Visualizing Network Graphs
Elements of Graph Visualization
Methods of Graph Visualization
Case Studies
Mapping 'Science'
Mapping the Internet
Mapping Dynamic Networks
Additional Related Topics and Reading
Exercises
Descriptive Analysis of Network Graph Characteristics
Introduction
Vertex and Edge Characteristics
Degree
Centrality
Characterizing Network Cohesion
Local Density
Connectivity
Graph Partitioning
Assortativity and Mixing
Case Study: Analysis of an Epileptic Seizure
Characterizing Dynamic Network Graphs
Additional Related Topics and Reading
Exercise
Sampling and Estimation in Network Graphs
Introduction
Background on Statistical Sampling Theory
Horvitz-Thompson Estimation for Totals
Estimation of Group Size
Common Network Graph Sampling Designs
Induced and Incident Subgraph Sampling
Star and Snowball Sampling
Link Tracing
Estimation of Totals in Network Graphs
Vertex Totals
Totals on Vertex Pairs
Totals of Higher Order
Effects of Design, Measurement, and Total
Estimation of Network Group Size
Other Network Graph Estimation Problems
Additional Related Topics and Reading
Exercises
Models for Network Graphs
Introduction
Random Graph Models
Classical Random Graph Models
Generalized Random Graph Models
Simulating Random Graph Models
Statistical Application of Random Graph Models
Small-World Models
The Watts-Strogatz Model
Other Small-World Network Models
Network Growth Models
Preferential Attachment Models
Copying Models
Fitting Network Growth Models
Exponential Random Graph Models
Model Specification
Fitting Exponential Random Graph Models
Goodness-of-Fit and Model Degeneracy
Case Study: Modeling Collaboration Among Lawyers
Challenges in Modeling Network Graphs
Additional Related Topics and Reading
Exercises
Network Topology Inference
Introduction
Link Prediction
Informal Scoring Methods
Probabilistic Classification Methods
Case Study: Predicting Lawyer Collaboration
Inference of Association Networks
Correlation Networks
Partial Correlation Networks
Gaussian Graphical Model Networks
Case Study: Inferring Genetic Regulatory Interactions
Tomographic Network Topology Inference
Tomographic Inference of Tree Topologies
Methods Based on Hierarchical Clustering
Likelihood-based Methods
Summarizing Collections of Trees
Case Study: Computer Network Topology Identification
Additional Related Topics and Reading
Exercises
Modeling and Prediction for Processes on Network Graphs
Introduction
Nearest Neighbor Prediction
Markov Random Fields
Markov Random Field Models
Inference and Prediction for Markov Random Fields
Related Probabilistic Models
Kernel-based Regression
Kernel Regression on Graphs
Designing Kernels on Graphs
Case Study: Predicting Protein Function
Modeling and Prediction for Dynamic Processes
Epidemic Processes: An Illustration
Other Dynamic Processes
Additional Related Topics and Reading
Exercises
Analysis of Network Flow Data
Introduction
Gravity Models
Model Specification
Inference for Gravity Models
Traffic Matrix Estimation
Static Methods
Dynamic Methods
Case Study: Internet Traffic Matrix Estimation
Estimation of Network Flow Costs
Link Costs from End-to-end Measurements
Path Costs from End-to-end Measurements
Additional Related Topics and Reading
Exercises
Graphical Models
Introduction
Defining Graphical Models
Directed Graphical Models
Undirected Graphical Models
Inference for Graphical Models
Additional Related Topics and Reading
Glossary of Notation
References
Author Index
Subject Index
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