Decoding Graphs
From Isomorphism to Neural Intelligence
Dr. Preeti Panwar
ISBN: 978-81-958714-7-6
Publisher/Imprint: World BIOLOGICA (India & USA)
Pages: 127
Format: e-Book
Language: English
Edition/Volume: 1st
© Year: 2025
Publication date: August 2025
Price
₹ 530
About the Book
In recent years, with the rise of deep learning models, researchers have begun asking a new question: Can neural networks — especially GNNs — learn what it means for two graphs to be the same? Can we train models that “feel” the structure of a graph the same way a human might spot similarities between two different networks?
This question connects age-old theory with cutting-edge practice. It blends algorithmic elegance with data-driven intelligence. And it opens the door to one of the most promising frontiers of artificial intelligence: building machines that can reason structurally, not just statistically.
This book, Decoding Graphs: From Isomorphism to Neural Intelligence, is a journey across that very bridge — from classical graph theory and algorithms to modern neural architectures and intelligent graph processing.
Table of Contents
Preface
Chapter 1 – The World of Graphs and Neural Intelligence
Introduction
The World of Graphs
Graph Isomorphic (GI)
Colour Refinement (CR)
Weisfeiler Leman (WL) Algorithm
Graph Neural Networks (GNN)
Chapter 2 – The Puzzle of Graph Isomorphism: Understanding Graph Isomorphism
The Challenge Behind Isomorphic Graphs
Algorithms and Their Applications
Applications in Chemistry and Biology
Network Analysis and Social Networks
Computer Science Applications
Implementation Challenges and Practical Considerations
Future Directions
Chapter 3 – Painting Graphs with Colour Refinement: The Basics of Colour Refinement
How Colour Refinement Works
Linking Colour to Graph Identity
Colour and Isomorphism: A Deeper Dive
Chapter 4 – The Weisfeiler-Leman Algorithm: A Giant Step from Simple to Higher-Order WL
How WL Transforms Graph Understanding
The Road to Powerful Discrimination
Chapter 5 – Meet Graph Neural Networks (GNNS)
What are GNNS?
How do GNNs Learn?
GNNs in Action: From Molecules to Social Networks
Chapter 6 – Exploring Powerful Ideas in GNN Research
Introduction
How Powerful Are GNNs?
Weisfeiler and Leman Go Neural
Provably Powerful Graph Networks
Nested GNNs and Subgraph Awareness
Key Takeaways from Groundbreaking Studies
Future Directions and Open Questions
Conclusion
Chapter 7 – The Future of Graph Intelligence
Introduction
Can GNNs Fully Solve Graph Isomorphism?
Merging Symbolic and Neural Worlds
Ethical, Scalable, and Practical AI for Graphs
Emerging Paradigms and Future Directions
Societal Transformation and Impact
Conclusion
Chapter 8 – The Science of Neural Networks
Highlighted Limitation with various variations of GNN and WL
Conclusion
Bibliography
About the Author
Dr. Preeti Panwar
Dr. Preeti Panwar, M.Sc., M.Phil., Ph.D., is working as the Head Department of Mathematics in Guru Nanak Khalsa College, Karnal (Haryana), India. She has eighteen years of teaching experience. She has published 15 research papers and book chapters in reputed national and international journals in areas of D-Spaces, Graph Neural Network and Group theory. Her areas of interest include Graph Theory,Group Theory and Group Rings.
Dr. Preeti has presented more than 15 research papers in National and International Conference and participated in more than 30 national and international conferences, seminars, faculty development programme and workshops. She is convener of one national seminar in Mathematics and organizing secretary of two national seminar. She has conducted one day workshop on NEP.
She is Gold Medalist in M.Sc. Mathematics and got tenth position in B.Sc. (Comp. Science).Under her supervision four students got gold medal in M.Sc. in different sessions.