Graph Spectra for Complex Networks Van Piet Van Mieghem is an English-language textbook that makes the connections between algebra and complex networks clear. It presents the spectral theory of graphs in a concise and well-structured way, with a strong focus on linear algebra.
The book builds the theory from the ground up, with linear algebra and polynomial theory at its core. Key matrix properties of the adjacency, Laplacian, and effective resistance matrices are discussed in detail. These insights are applied to complex networks to explain the behavior and properties of real-world networks.
In addition to theoretical foundations, this second edition also covers new topics such as the pseudoinverse of the Laplacian and spectral sparsification. Practical applications, including graph networks and linear processes, are also addressed.
This textbook aligns with fields such as combinatorics, graph theory, and communication networks, and provides a solid foundation for higher education and research focused on complex networks and algebra.