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Springer.Statistical Analysis of Network Data with R.(Use R!).20....pdf
Cover
Preface
Contents
Biographies
Chapter 1 Introduction
1.1 Why Networks?
1.2 Types of Network Analysis
1.2.1 Visualizing and Characterizing Networks
1.2.2 Network Modeling and Inference
1.2.3 Network Processes
1.3 Why Use R for Network Analysis?
1.4 About This Book
1.5 About the R code
Chapter 2 Manipulating Network Data
2.1 Introduction
2.2 Creating Network Graphs
2.2.1 Undirected and Directed Graphs
2.2.2 Representations for Graphs
2.2.3 Operations on Graphs
2.3 Decorating Network Graphs
2.3.1 Vertex, Edge, and Graph Attributes
2.3.2 Using Data Frames
2.4 Talking About Graphs
2.4.1 Basic Graph Concepts
2.4.2 Special Types of Graphs
2.5 Additional Reading
Chapter 3 Visualizing Network Data
3.1 Introduction
3.2 Elements of Graph Visualization
3.3 Graph Layouts
3.4 Decorating Graph Layouts
3.5 Visualizing Large Networks
3.6 Using Visualization Tools Outside of R
3.7 Additional Reading
Chapter 4 Descriptive Analysis of Network Graph Characteristics
4.1 Introduction
4.2 Vertex and Edge Characteristics
4.2.1 Vertex Degree
4.2.2 Vertex Centrality
4.2.3 Characterizing Edges
4.3 Characterizing Network Cohesion
4.3.1 Subgraphs and Censuses
4.3.2 Density and Related Notions of Relative Frequency
4.3.3 Connectivity, Cuts, and Flows
4.4 Graph Partitioning
4.4.1 Hierarchical Clustering
4.4.2 Spectral Partitioning
4.4.3 Validation of Graph Partitioning
4.5 Assortativity and Mixing
4.6 Additional Reading
Chapter 5 Mathematical Models for Network Graphs
5.1 Introduction
5.2 Classical Random Graph Models
5.3 Generalized Random Graph Models
5.4 Network Graph Models Based on Mechanisms
5.4.1 Small-World Models
5.4.2 Preferential Attachment Models
5.5 Assessing Significance of Network Graph Characteristics
5.5.1 Assessing the Number of Communities in a Network
5.5.2 Assessing Small World Properties
5.6 Additional Reading
Chapter 6 Statistical Models for Network Graphs
6.1 Introduction
6.2 Exponential Random Graph Models
6.2.1 General Formulation
6.2.2 Specifying a Model
6.2.3 Model Fitting
6.2.4 Goodness-of-Fit
6.3 Network Block Models
6.3.1 Model Specification
6.3.2 Model Fitting
6.3.3 Goodness-of-Fit
6.4 Latent Network Models
6.4.1 General Formulation
6.4.2 Specifying the Latent Effects
6.4.3 Model Fitting
6.4.4 Goodness-of-Fit
6.5 Additional Reading
Chapter 7 Network Topology Inference
7.1 Introduction
7.2 Link Prediction
7.3 Association Network Inference
7.3.1 Correlation Networks
7.3.2 Partial Correlation Networks
7.3.3 Gaussian Graphical Model Networks
7.4 Tomographic Network Topology Inference
7.4.1 Constraining the Problem: Tree Topologies
7.4.2 Tomographic Inference of Tree Topologies:An Illustration
7.5 Additional Reading
Chapter 8 Modeling and Prediction for Processes on Network Graphs
8.1 Introduction
8.2 Nearest Neighbor Methods
8.3 Markov Random Fields
8.3.1 General Characterization
8.3.2 Auto-Logistic Models
8.3.3 Inference and Prediction for Auto-logistic Models
8.3.4 Goodness of Fit
8.4 Kernel Methods
8.4.1 Designing Kernels on Graphs
8.4.2 Kernel Regression on Graphs
8.5 Modeling and Prediction for Dynamic Processes
8.5.1 Epidemic Processes: An Illustration
8.6 Additional Reading
Chapter 9 Analysis of Network Flow Data
9.1 Introduction
9.2 Modeling Network Flows: Gravity Models
9.2.1 Model Specification
9.2.2 Inference for Gravity Models
9.3 Predicting Network Flows: Traffic Matrix Estimation
9.3.1 An Ill-Posed Inverse Problem
9.3.2 The Tomogravity Method
9.4 Additional Reading
Chapter 10 Dynamic Networks
10.1 Introduction
10.2 Representation and Manipulation of Dynamic Networks
10.3 Visualization of Dynamic Networks
10.4 Characterization of Dynamic Networks
10.5 Modeling Dynamic Networks
References
Index
UseR!
Eric D. Kolaczyk
Gábor Csárdi
Statistical
Analysis of
Network Data
with R
Use R!
Series Editors:
Robert Gentleman Kurt Hornik Giovanni Parmigiani
For further volumes:
http://www.springer.com/series/6991
Use R!
Albert: Bayesian Computation with R (2nd ed. 2009)
Bivand/Pebesma/G´omez-Rubio: Applied Spatial Data Analysis with R (2nd ed.
2013)
Cook/Swayne: Interactive and Dynamic Graphics for Data Analysis:
With R and GGobi
Hahne/Huber/Gentleman/Falcon: Bioconductor Case Studies
Paradis: Analysis of Phylogenetics and Evolution with R (2nd ed. 2012)
Pfaff: Analysis of Integrated and Cointegrated Time Series with R (2nd ed. 2008)
Sarkar: Lattice: Multivariate Data Visualization with R
Spector: Data Manipulation with R
Eric D. Kolaczyk • G´abor Cs´ardi
Statistical Analysis of
Network Data with R
123
Eric D. Kolaczyk
Department of Mathematics and Statistics
Boston University Professor
Boston, MA, USA
G´abor Cs´ardi
Department of Statistics
Harvard University Research Associate
Cambridge, MA, USA
ISSN 2197-5736
ISBN 978-1-4939-0982-7
DOI 10.1007/978-1-4939-0983-4
Springer New York Heidelberg Dordrecht London
ISSN 2197-5744 (electronic)
ISBN 978-1-4939-0983-4 (eBook)
Library of Congress Control Number: 2014936989
© Springer Science+Business Media New York 2014
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection
with reviews or scholarly analysis or material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of
this publication or parts thereof is permitted only under the provisions of the Copyright Law of the
Publisher’s location, in its current version, and permission for use must always be obtained from Springer.
Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations
are liable to prosecution under the respective Copyright Law.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
While the advice and information in this book are believed to be true and accurate at the date of pub-
lication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any
errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect
to the material contained herein.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Pour Jos´ee, sans qui ce livre n’aurait pas vu
le jour—E.D.K.
Z-nak, a gy´em´ant´ert ´es az arany´ert—G.CS.
Preface
Networks and network analysis are arguably one of the largest recent growth areas
in the quantitative sciences. Despite roots in social network analysis going back
to the 1930s and roots in graph theory going back centuries, the phenomenal rise
and popularity of the modern field of ‘network science’, as it is sometimes called,
is something that likely could not have been predicted 10–15 years ago. Networks
have permeated everyday life, far beyond the realm of research and methodology,
through now-familiar realities like the Internet, social networks, viral marketing,
and more.
Measurement and data analysis are integral components of network research. As
a result, there is a critical need for all sorts of statistics for network analysis, both
common and sophisticated, ranging from applications, to methodology, to theory.
As with other areas of statistics, there are both descriptive and inferential statistical
techniques available, aimed at addressing a host of network-related tasks, including
basic visualization and characterization of network structure; sampling, modeling,
and inference of network topology; and modeling and prediction of network-indexed
processes, both static and dynamic.
Software for performing many such network-related analyses is now available
in various languages and environments, across different platforms. Not surprisingly,
the R community has been particularly active in the development of software for do-
ing statistical analysis of network data. As of this writing there are already dozens
of contributed R packages devoted to some aspect of network analysis. Together,
these packages address tasks ranging from standard manipulation, visualization, and
characterization of network data (e.g., igraph, network, and sna), to modeling of
networks (e.g., igraph, eigenmodel, ergm, and mixer), to network topology infer-
ence (e.g., glasso and huge). In addition, there is a great deal of analysis that can be
done using tools and functions from the R base package.
In this book we aim to provide an easily accessible introduction to the statistical
analysis of network data, by way of the R programming language. As a result, this
book is not, on the one hand, a detailed manual for using the various R packages en-
countered herein, nor, on the other hand, does it provide exhaustive coverage of the
conceptual and technical foundations of the topic area. Rather, we have attempted
vii
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