Mathematics of Networks

Mathematics of Networks: Modulus Theory and Convex Optimization explores the question: What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete graphs? This book navigates the rich landscape of p-modulus on graphs, demonstrating how this theory elegantly connects concepts from graph theory, probability, and convex optimization. This book is ideal for anyone seeking a deeper understanding of the theoretical foundations of network analysis and applied graph theory. It serves as an excellent primary text or reference for graduate and advanced undergraduate courses across multiple disciplines, including mathematics, data science, and engineering, particularly those focusing on network analysis, applied graph theory, optimization, and related areas. Features: Accessible to students with a solid foundation in multivariable calculus and linear algebra. Broad interdisciplinary appeal, relevant to mathematics, data science, and engineering curricula. Numerous engaging exercises.