Mathematics of Networks: Modulus Theory and Convex Optimization

Mathematics of Networks: Modulus Theory and Convex Optimization is a book that seeks to answer the question: “What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete graphs?” As the book leads readers through the rich landscape of p-modulus on graphs, it is shown that the theory ties together many beautiful concepts from graph theory, probability, and convex optimization. The book ought to be of interest to anyone seeking to deepen their understanding of the theoretical underpinnings of network analysis and applied graph theory. As such, it can be used as either a primary text or a useful reference for graduate courses on topics related to network analysis and applied graph theory, and even for some advanced undergraduates. Features • Accessible to anyone with a strong grasp of multivariable calculus and linear algebra • Broad interdisciplinary appeal • Numerous engaging exercises