Algebraic Graph Algorithms: A Practical Guide Using Python

This textbook covers the design and implementation of algebraic graph algorithms, focusing on matroids and parallel processing. It assumes a background in graph theory and provides example code in pseudocode and case studies in Python and MPI.

Format: Paperback / softback
Length: 221 pages
Publication date: 18 November 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook delves into the intricate realm of designing and implementing fundamental algebraic graph algorithms, as well as advanced algorithms tailored for complex networks. By leveraging the power of matroids whenever feasible, the text offers a comprehensive exploration of graph theory and its applications.

The central focus of the book lies in the development of a versatile parallel matrix algorithm kernel, designed to facilitate efficient parallel processing of algebraic graph algorithms. This kernel is presented in pseudocode, accompanied by comprehensive case studies implemented in Python and MPI. The text assumes a foundational understanding of graph theory and/or graph algorithms, providing a solid foundation for readers to delve into the complexities of algebraic graph processing.

In Chapter 1, the authors introduce the fundamental concepts and principles of algebraic graph algorithms. They begin by discussing the basic graph structures, such as vertices, edges, and graphs, and then delve into the theory of matroids, a powerful tool for graph representation and analysis. The chapter also highlights the importance of graph algorithms in various real-world applications, including network flow optimization, social network analysis, and machine learning.

Chapter 2 focuses on the design and implementation of basic algebraic graph algorithms. The authors introduce various algorithms, including shortest path algorithms, maximum flow algorithms, and graph isomorphism algorithms, and explain their underlying principles and computational complexities. They also discuss the use of graph representations, such as adjacency lists and adjacency matrices, to efficiently solve graph problems.

Chapter 3 delves into the realm of algebraic graph algorithms for complex networks. The authors introduce the concept of graph embedding, which involves mapping complex networks into a lower-dimensional space for efficient analysis and visualization. They discuss various embedding techniques, including spectral embedding, random walk embedding, and deep learning-based embedding, and their applications in network analysis and visualization.

Chapter 4 presents the parallel matrix algorithm kernel, which forms the core of the book. The authors introduce the concept of parallel processing and discuss the challenges associated with it. They then present the design and implementation of the parallel matrix algorithm kernel, including its data structures, communication protocols, and execution strategies. The kernel is designed to be scalable and efficient, enabling the processing of large-scale algebraic graph algorithms in parallel.

Chapter 5 showcases the application of the parallel matrix algorithm kernel in various case studies. The authors present real-world graph problems, such as network flow optimization, community detection, and graph isomorphism, and demonstrate how the kernel can be used to solve these problems efficiently in parallel. They also discuss the performance analysis and optimization of the kernel, and provide insights into the scalability and efficiency of parallel graph processing.

Chapter 6 concludes the book by discussing the future directions and potential applications of algebraic graph algorithms. The authors highlight the growing importance of graph data and the need for efficient algorithms to analyze and manipulate it. They also discuss the potential of machine learning and deep learning techniques in graph analysis and visualization.

In summary, this textbook provides a comprehensive and in-depth exploration of algebraic graph algorithms, with a particular emphasis on their design and implementation for complex networks. By leveraging matroids and parallel processing techniques, the book offers readers a powerful toolset for analyzing and manipulating graph data in a variety of real-world applications. Whether you are a researcher, engineer, or data analyst, this textbook is an invaluable resource for advancing your understanding of algebraic graph algorithms and their applications.

Weight: 367g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030878856
Edition number: 1st ed. 2021