Network Theory Through Linear Algebra
A Mathematical Framework for Understanding Complex Systems and Graph Structures
Many people approach network theory as a purely graph-theoretic discipline, missing the profound insights that linear algebra brings to understanding complex systems. Without the right mathematical framework, analyzing large networks becomes computationally intractable and conceptually opaque. This book bridges that gap by showing you how matrices, eigenvalues, and linear transformations unlock the hidden structure of networks. You'll discover how adjacency and Laplacian matrices transform network questions into solvable linear algebra problems. Through spectral analysis, you'll learn to identify communities, measure centrality, and predict network behavior. The book connects abstract mathematical concepts to concrete applications, from ranking web pages to modeling epidemic spread. Each chapter builds systematically on linear algebra foundations while introducing network-specific techniques. You'll work through the mathematics of random walks, explore how eigenvalues reveal network connectivity, and understand why certain networks are robust while others are fragile. By the end, you'll possess a powerful toolkit for analyzing any networked system—from social networks to neural circuits—with mathematical rigor and computational efficiency.
Est. Length
222 pages (12 chapters)
Language
English
Publication date
Oct 29, 2025
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