Brain Network Analysis

This tutorial reference serves as a coherent overview of various statistical and mathematical approaches used in brain network analysis, where modeling the complex structures and functions of the human brain often poses many unique computational and statistical challenges. This book fills a gap as a textbook for graduate students while simultaneously articulating important and technically challenging topics. Whereas most available books are graph theory-centric, this text introduces techniques arising from graph theory and expands to include other different models in its discussion on network science, regression, and algebraic topology. Links are included to the sample data and codes used in generating the book's results and figures, helping to empower methodological understanding in a manner immediately usable to both researchers and students. Cover 1 Front Matter 3 Brain Network Analysis 5 Copyright 6 Dedication 7 Contents 9 Preface 13 1 Statistical Preliminary 15 2 Brain Network Nodes and Edges 41 3 Graph Theory 75 4 Correlation Networks 90 5 Big Brain Network Data 122 6 Network Simulations 143 7 Persistent Homology 170 8 Diffusions on Graphs 194 9 Sparse Networks 221 10 Brain Network Distances 240 11 Combinatorial Inferences for Networks 260 12 Series Expansion of Connectivity Matrices 283 13 Dynamic Network Models 306 Bibliography 316 Index 340 This tutorial reference provides a coherent overview of statistical and mathematical approaches used in brain network analysis. It goes beyond graph theory to explore different models in network science, regression, and algebraic topology, empowering methodological understanding in a manner immediately usable to both researchers and students.