Fundamentals of Brain Network Analysis

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 illustrating how they can be practically applied in diverse 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.

Winner of the 2017 PROSE Award in Biomedicine & Neuroscience and the 2017 British Medical Association (BMA) Award in Neurology Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systemsComprehensively 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 neuroscienceDesigned 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

• Author Biographies
• Foreword
• Acknowledgments
• Chapter 1: An Introduction to Brain Networks
  • Abstract
  • 1.1 Graphs as Models for Complex Systems
  • 1.2 Graph Theory and the Brain
  • 1.3 Are graph theory and connectomics useful?
  • 1.4 Summary
• Chapter 2: Nodes and Edges
  • Abstract
  • 2.1 Microscale Connectomics
  • 2.2 Mesoscale Connectomics
  • 2.3 Macroscale Connectomics
  • 2.4 Summary
• Chapter 3: Connectivity Matrices and Brain Graphs
  • Abstract
  • 3.1 The Connectivity Matrix
  • 3.2 The Adjacency Matrix
  • 3.3 Network Visualization
  • 3.4 What Type of Network Is a Connectome?
  • 3.5 Summary
• Chapter 4: Node Degree and Strength
  • Abstract
  • 4.1 Measures of Node Connectivity
  • 4.2 Degree Distributions
  • 4.3 Weight Distributions
  • 4.4 Summary
• Chapter 5: Centrality and Hubs
  • Abstract
  • 5.1 Centrality
  • 5.2 Identifying Hub Nodes
  • 5.3 Summary
• Chapter 6: Components, Cores, and Clubs
  • Abstract
  • 6.1 Connected Components
  • 6.2 Core-Periphery Organization
  • 6.3 Rich Clubs
  • 6.4 Summary
• Chapter 7: Paths, Diffusion, and Navigation
  • Abstract
  • 7.1 Walks, Trails, Paths, and Cycles
  • 7.2 Shortest Path Routing
  • 7.3 Diffusion Processes
  • 7.4 Navigation and Other Models of Neural Communication
  • 7.5 Summary
• Chapter 8: Motifs, Small Worlds, and Network Economy
  • Abstract
  • 8.1 Network Motifs
  • 8.2 Clustering, Degeneracy, and Small Worlds
  • 8.3 Network Economy
  • 8.4 Summary
• Chapter 9: Modularity
  • Abstract
  • 9.1 Defining Modules
  • 9.2 Node Roles
  • 9.3 Comparing and Aggregating Network Partitions
  • 9.4 Dynamic Modularity
  • 9.5 Summary
• Chapter 10: Null Models
  • Abstract
  • 10.1 Generative Null Models
  • 10.2 Null Networks from Rewiring Connections
  • 10.3 Functional Connectivity Networks
  • 10.4 Summary
• Chapter 11: Statistical Connectomics
  • Abstract
  • 11.1 Matrix Thresholding
  • 11.2 Statistical Inference on Brain Networks
  • 11.3 Multivariate Approaches
  • 11.4 Summary
• Glossary
• References
• Index