Graph Algorithms: A Classic Computer Science Textbook on Network Flows, Depth-First Search, and Planarity by Shimon Even

Introduction

Graph algorithms lie at the heart of modern computing, powering everything from social networks and route planning to network flow optimisation and circuit design. For decades, Shimon Even’s Graph Algorithms has been the definitive guide for students and professionals who want a rigorous yet accessible foundation in this essential subject. Now thoroughly revised and updated, this second edition from Cambridge University Press brings classic theory into the present day, making it an indispensable resource for Indian computer science students, software engineers, and competitive programmers.

Book Overview

Originally published in 1979, Shimon Even’s Graph Algorithms was a landmark text that shaped an entire generation of algorithm designers. This second edition, featuring a foreword by Richard M. Karp and extensive notes by Andrew V. Goldberg, preserves the clarity and depth of the original while incorporating modern insights. The book begins with fundamental concepts such as graphs, shortest paths, trees, depth-first search, and breadth-first search. It then delves into the core of network flows and their diverse applications, before concluding with planar graphs and graph planarity testing. Every algorithm is explained in a formal yet intuitive style, with emphasis on correctness proofs and efficient implementation.

Key Highlights

• Revised and updated edition of a classic algorithms textbook, with new notes and commentary by Andrew V. Goldberg
• Foreword by Richard M. Karp, a Turing Award winner and pioneer in algorithm analysis
• Clear, step-by-step explanations of graph algorithms, from basics to advanced topics
• Focus on network flows, including max-flow min-cut theorem, augmenting paths, and applications
• In-depth coverage of planarity testing – a rare and valuable topic in modern algorithm books
• Rigorous yet accessible – ideal for self-study and classroom use

Inside the Book

The book is structured to build understanding progressively. Early chapters cover essential graph theory and search techniques, including BFS, DFS, and shortest-path algorithms like Dijkstra’s and Bellman-Ford. The middle section is devoted to network flows: the Ford-Fulkerson method, Edmonds-Karp algorithm, and applications such as bipartite matching, circulation problems, and connectivity. The final chapters explore planar graphs, Euler’s formula, and the Hopcroft-Tarjan planarity testing algorithm – a topic rarely treated in such depth. Each chapter includes carefully chosen exercises that reinforce learning and challenge the reader to think algorithmically.

Key Topics

• Graph representation and basic properties
• Breadth-first search and depth-first search
• Shortest paths in weighted and unweighted graphs
• Minimum spanning trees (Prim’s and Kruskal’s algorithms)
• Maximum flow and minimum cut
• Applications of network flows: matching, vertex connectivity, edge connectivity
• Planar graphs: characterisation, dual graphs, and planarity testing
• Algorithms for testing graph planarity (Hopcroft-Tarjan method)

Reader Benefits

By studying this book, readers will gain a deep, principled understanding of graph algorithms that goes beyond rote memorisation. The focus on correctness proofs and algorithmic reasoning prepares students for advanced courses in theoretical computer science, while the practical examples and applications make it valuable for working professionals. Indian students preparing for GATE, UGC-NET, or competitive programming contests will find the clear exposition and classic algorithms directly applicable. The book also serves as an excellent reference for researchers and practitioners who need to implement efficient graph algorithms in fields such as operations research, network design, and data science.

Learning Outcomes

• Master the fundamental graph search techniques (BFS, DFS) and their applications
• Understand and implement shortest-path algorithms for various graph types
• Analyse and design network flow algorithms with confidence
• Apply flow theory to solve real-world problems like matching and connectivity
• Comprehend the theory of planar graphs and test graph planarity algorithmically
• Develop rigorous algorithmic thinking through proofs and complexity analysis

Who Should Read

This book is ideal for undergraduate and postgraduate computer science students in India who have taken a basic data structures and algorithms course. It is also highly recommended for software engineers, data scientists, and researchers who want to strengthen their algorithmic foundation. Competitive programmers will appreciate the classic algorithms and their efficient implementations. Additionally, instructors teaching graph theory or advanced algorithms will find this an excellent textbook for semester-long courses.

About the Author

Shimon Even was a pioneering computer scientist and professor at the Technion – Israel Institute of Technology. His work in graph algorithms, network flows, and cryptography has had a lasting impact on the field. He authored several influential textbooks and mentored generations of students, including Andrew V. Goldberg, who contributed extensively to this revised edition. Even’s ability to present complex ideas with elegance and precision is evident throughout this book.

About the Publisher

Cambridge University Press is a world-renowned academic publisher with a legacy of excellence spanning over four centuries. Known for its rigorous editorial standards and commitment to scholarly quality, Cambridge University Press publishes textbooks and reference works that are trusted by students and academics worldwide. This edition of Graph Algorithms upholds that tradition, offering Indian readers a premium hardcover volume that will endure years of study and reference.

Conclusion

Whether you are a student beginning your journey into graph theory or a seasoned professional seeking to deepen your algorithmic expertise, Shimon Even’s Graph Algorithms is a timeless investment. With its clear exposition, rigorous proofs, and comprehensive coverage of network flows and planarity, this second edition remains the gold standard for graph algorithm textbooks. Add this essential volume to your library and master the algorithms that drive the digital world.