Fundamentals of brain network analysis / Alex Fornito, Andrew Zalesky, Edward T Bullmore.

Format:

Book

Author/Creator:

Fornito, Alex, author.

Zalesky, Andrew, author.

Bullmore, Edward T., author.

Language:

English

Subjects (All):

Neural networks (Neurobiology).

Neural circuitry.

Brain.

Physical Description:

xvii, 476 pages : color illustrations ; 24 cm

Place of Publication:

Amsterdam ; Boston : Elsevier/Academic Press, [2016]

Summary:

Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates, and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by demonstrating how they can be practically applied across many different areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. Key Features: Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems, Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience, Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain Book jacket.

Contents:

Chapter 1 An Introduction to Brain Networks 1

1.1 Graphs as Models for Complex Systems 4

1.1.1 A Brief History of Graph Theory 5

1.1.2 Space, Time, and Topology 11

1.2 Graph Theory and the Brain 13

1.2.1 The Neuron Theory and Connectivity at the Microscale 13

1.2.2 Clinicopathological Correlations and Connectivity at the Macroscale 15

1.2.3 The Dawn of Connectomics 18

1.2.4 Neuroimaging and Human Connectomics 22

1.2.5 Back to Basics: From Macro to Meso and Micro Connectomics 30

1.3 Are Graph Theory and Connectomics Useful? 33

1.4 Summary 34

Chapter 2 Nodes and Edges 37

2.1 Microscale Connectomics 42

2.1.1 Structural Connectivity at the Microscale 42

2.1.2 Functional Connectivity at the Microscale 48

2.2 Mesoscale Connectomics 56

2.2.1 Structural Connectivity at the Mesoscale 56

2.2.2 Functional Connectivity at the Mesoscale 66

2.3 Macroscale Connectomics 70

2.3.1 Defining Nodes at the Macroscale 71

2.3.2 Structural Connectivity at the Macroscale 77

2.3.3 Functional Connectivity at the Macroscale 82

2.4 Summary 87

Chapter 3 Connectivity Matrices and Brain Graphs 89

3.1 The Connectivity Matrix 89

3.1.1 Diagonal and Off-Diagonal Elements 90

3.1.2 Directionality 91

3.1.3 Connectivity Weights 93

3.1.4 Sparse Matrices 94

3.2 The Adjacency Matrix 95

3.2.1 Thresholding 97

3.2.2 Binarization 97

3.2.3 Network Density and Weight 98

3.3 Network Visualization 101

3.3.1 Visualizing the Adjacency Matrix 102

3.3.2 Visualizing Brain Graphs 104

3.4 What Type of Network Is a Connectome? 108

3.5 Summary 113

Chapter 4 Node Degree and Strength 115

4.1 Measures of Node Connectivity 116

4.1.1 Node Degree 117

4.1.2 Node Strength 118

4.1.3 Node Degree and Network Density 120

4.2 Degree Distributions 121

4.2.1 Single-Scale Distributions 122

4.2.2 Scale-Free Distributions 125

4.2.3 Broad-Scale Distributions 129

4.3 Weight Distributions 132

4.3.1 The Lognormal Distribution 132

4.4 Summary 136

Chapter 5 Centrality and Hubs 137

5.1 Centrality 137

5.1.1 Degree-Based Measures of Centrality 139

5.1.2 Closeness Centrality 147

5.1.3 Betweenness Centrality 150

5.1.4 Delta Centrality 151

5.1.5 Characterizing Centrality in Brain Networks 152

5.2 Identifying Hub Nodes 156

5.2.1 Classifying Hubs Based on Degree and Centrality 156

5.2.2 Consensus Classification of Hubs 157

5.2.3 Module-Based Role Classification 160

5.3 Summary 161

Chapter 6 Components, Cores, and Clubs 163

6.1 Connected Components 164

6.1.1 Components in Undirected Networks 167

6.1.2 Components in Directed Networks 168

6.1.3 Percolation and Robustness 172

6.1.4 Components and Group Differences in Networks 177

6.2 Core-Periphery Organization 179

6.2.1 Maximal Cliques 180

6.2.2 k-Cores and s-Cores 180

6.2.3 Model-Based Decomposition 185

6.2.4 Knotty Centrality 189

6.2.5 Bow-Tie Structure 193

6.3 Rich Clubs 194

6.3.1 The Unweighted Rich-Club Coefficient 195

6.3.2 The Weighted Rich-Club Coefficient 198

6.3.3 Rich-Clubs in Brain Networks 200

6.3.4 Assortativity 204

6.4 Summary 206

Chapter 7 Paths, Diffusion, and Navigation 207

7.1 Walks, Trails, Paths, and Cycles 210

7.1.1 Shortest Paths 211

7.1.2 Finding Shortest Paths 214

7.1.3 Shortest Paths and Negative Edges 217

7.2 Shortest Path Routing 223

7.2.1 Characteristic Path Length 223

7.2.2 Global and Nodal Efficiency 225

7.3 Diffusion Processes 228

7.3.1 Search Information and Path Transitivity 230

7.3.2 Measures of Diffusion Efficiency 234

7.3.3 Communicability 244

7.4 Navigation and Other Models of Neural Communication 245

7.4.1 Navigation of Small-World Networks 246

7.4.2 Internet and Computer Analogies 250

7.5 Summary 254

Chapter 8 Motifs, Small Worlds, and Network Economy 257

8.1 Network Motifs 257

8.1.1 Node Motifs 259

8.1.2 Path Motifs 265

8.2 Clustering, Degeneracy, and Small Worlds 268

8.2.1 The Clustering Coefficient 269

8.2.2 Redundancy, Degeneracy, and Structural Equivalence 272

8.2.3 Small Worlds 281

8.3 Network Economy 287

8.3.1 Wiring Cost Optimization in Nervous Systems 288

8.3.2 Cost-Efficiency Trade-Offs 291

8.3.3 Rentian Scaling 296

8.4 Summary 301

Chapter 9 Modularity 303

9.1 Defining Modules 307

9.1.1 Agglomerative and Divisive Clustering 308

9.1.2 Quantifying Modularity 311

9.1.3 Maximizing Modularity 316

9.2 Node Roles 325

9.2.1 Cartographic Classification of Nodes 325

9.2.2 Node Roles in Brain Networks 331

9.3 Comparing and Aggregating Network Partitions 334

9.3.1 Comparing Two Partitions 335

9.3.2 Comparing Populations of Partitions 339

9.3.3 Consensus Clustering 340

9.4 Dynamic Modularity 346

9.4.1 Multilayer Modularity 347

9.4.2 Dynamic Modularity of Brain Networks 351

9.5 Summary 353

Chapter 10 Null Models 355

10.1 Generative Null Models 357

10.1.1 Erdös-Rényi Networks 361

10.1.2 Watts-Strogatz Networks 363

10.1.3 Barabási-Albert Networks 364

10.2 Null Networks from Rewiring Connections 367

10.2.1 Maslov-Sneppen Rewiring 367

10.2.2 Rewiring Connections in Weighted and Signed Networks 369

10.2.3 Lattice Null Networks 371

10.2.4 Spatial Embedding 372

10.3 Functional Connectivity Networks 375

10.3.1 Null models for Correlation-Based Networks 377

10.4 Summary 380

Chapter 11 Statistical Connectomics 383

11.1 Matrix Thresholding 384

11.1.1 Global Thresholding 384

11.1.2 Network Fragmentation 388

11.1.3 Local Thresholding 388

11.1.4 Normalization with Reference Networks 391

11.1.5 Integration and Area Under the Curve 392

11.1.6 Multiresolution Thresholding 393

11.2 Statistical Inference on Brain Networks 396

11.2.1 Global Testing 397

11.2.2 Mass Univariate Testing 397

11.2.3 Strong Control of Familywise Errors 398

11.2.4 Multiple Comparisons Under Dependence 401

11.2.5 The False Discovery Rate 403

11.2.6 The Network-Based Statistic 404

11.2.7 Spatial Pairwise Clustering 408

11.2.8 The Screening-Filtering Method 411

11.2.9 Sum of Powered Score 412

11.3 Multivariate Approaches 413

11.3.1 Support Vector Machines 414

11.3.2 Other Multivariate Approaches 417

11.4 Summary 418.

Notes:

Includes bibliographical references and index.

ISBN:

9780124079083

0124079083

OCLC:

943431396