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Graph Theory with AI Applications VOL-1

Algorithms and Modern Neural Approaches

This book is 100% completeLast updated on 2026-06-12

Graphs are everywhere.

From social media networks and recommendation systems to autonomous vehicles, cybersecurity platforms, and modern artificial intelligence, graph structures have become the language of connected data.

But how do machines understand relationships?

How do search engines rank billions of pages?

How do recommendation systems predict what users will like next?

How do AI systems learn from complex networks?

Graph Theory with AI Applications: Foundations, Algorithms, and Modern Neural Approaches (VOL-1) provides the answers.

This book takes readers on a structured journey through graph fundamentals, graph algorithms, shortest path methods, network optimization, social network analytics, community detection, and graph mining techniques. Designed for students, researchers, educators, and professionals, it combines mathematical foundations with practical AI applications.

If you want to understand the science behind connected intelligence and prepare yourself for the future of Graph Neural Networks and AI-driven graph learning, this book is your starting point.

Discover the foundations. Master the algorithms. Build the future of Graph AI.

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About the Book

Graph Theory with AI Applications: Foundations, Algorithms, and Modern Neural Approaches (VOL-1) is a comprehensive academic and professional guide that explores the powerful intersection of Graph Theory and Artificial Intelligence. In today's data-driven world, many real-world systems—from social networks and communication infrastructures to recommendation engines and autonomous systems—are naturally represented as graphs. Understanding graph structures and algorithms has therefore become essential for students, researchers, and AI practitioners.

This volume provides a strong foundation in classical graph theory while gradually connecting these concepts to modern AI applications. Readers begin with the fundamentals of graph structures, graph representations, traversal algorithms, shortest-path techniques, spanning trees, network flows, and graph optimization methods. The book then extends these foundations into social network analysis, community detection, centrality measures, link prediction, and graph mining.

Unlike traditional graph theory textbooks, this work emphasizes practical relevance and computational applications. Each chapter demonstrates how graph-based methods are used in robotics, navigation systems, recommendation engines, fraud detection, search algorithms, and intelligent decision-making systems.

Written in a structured and learner-friendly manner, the book combines mathematical rigor, algorithmic understanding, and application-oriented insights. It serves as an ideal resource for undergraduate and postgraduate students, AI researchers, data scientists, software engineers, and professionals interested in network analytics and intelligent systems.

As the first volume of a two-volume series, this book establishes the theoretical and algorithmic foundations required for understanding advanced Graph Neural Networks (GNNs), graph embeddings, and graph-based machine learning techniques that are covered in Volume II.

Whether you are preparing for academic examinations, conducting research, or building intelligent graph-based applications, this book provides the knowledge and skills necessary to navigate the rapidly evolving world of Graph AI.

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About the Author

Anshuman Mishra

Anshuman Kumar Mishra, M.Tech (Computer Science) Assistant Professor, Doranda College, Ranchi University

Prolific Author of 50+ Books on AI, Machine Learning & Computer Science | 20+ Years Experience

Anshuman Kumar Mishra is a dedicated educator, researcher, and highly prolific author with over 20 years of experience in Computer Science and Information Technology. Holding an M.Tech in Computer Science from BIT Mesra, he brings a rare combination of academic depth and practical teaching expertise.

Currently serving as Assistant Professor at Doranda College under Ranchi University, he has mentored thousands of students, helping them build strong foundations in programming, data science, and artificial intelligence. His student-centric teaching style emphasizes conceptual clarity, hands-on practice, and real-world application.

Anshuman is a prolific author with more than 50 books published across a wide spectrum of computer science and emerging technology domains. From foundational programming languages to advanced topics in Artificial Intelligence, Machine Learning, Reinforcement Learning, Decision Theory, and Computer Vision — his books are widely appreciated by students, educators, and professionals for their clear explanations, strong theoretical foundation, and practical approach.

His extensive body of work reflects his deep commitment to making complex subjects accessible and meaningful for learners at all levels. He is particularly recognized for creating well-structured learning paths that help readers progress from beginner to advanced levels with confidence.

Driven by the mission to democratize quality technical education, Anshuman continues to write and update books that bridge the gap between academic theory and industry practice.

When not teaching or writing, he actively follows and explores new developments in AI, Quantum Machine Learning, and Ethical Intelligence systems.

Contents

Table of Contents

Graph Theory with AI Applications: Foundations, Algorithms, and Modern Neural Approaches VOL-1 ________________________________________ Table of Contents ________________________________________ Part I: Foundations of Graph Theory Chapter 1: Introduction to Graph Theory 1-25 1.1 What is a Graph? 1.2 Historical Evolution of Graph Theory 1.3 Graphs in Modern Computing and AI 1.4 Directed vs Undirected Graphs 1.5 Weighted, Unweighted, and Labeled Graphs 1.6 Static vs Dynamic Graphs 1.7 Applications in Real-World Problems ________________________________________ Chapter 2: Graph Terminologies and Basic Properties 26-47 2.1 Degree, Path, Cycle, Connectivity 2.2 Trees and Forests 2.3 Cliques, Independent Sets, Cut Vertices 2.4 Bipartite Graphs and Matching 2.5 Isomorphism & Automorphism 2.6 Graph Representations: Matrix, List, Adjacent Structure ________________________________________ Chapter 3: Matrix Representations and Computations 48-72 3.1 Adjacency Matrix 3.2 Incidence Matrix 3.3 Laplacian Matrix 3.4 Spectral Properties of Graphs 3.5 Eigenvalues and Graph Connectivity 3.6 Applications of Graph Matrices in AI ________________________________________ Chapter 4: Graph Traversal Algorithms 73-98 4.1 Breadth-First Search (BFS) 4.2 Depth-First Search (DFS) 4.3 Bidirectional Search 4.4 Topological Sorting 4.5 Connected Component Detection 4.6 AI Applications of Graph Traversal ________________________________________ Part II: Classical Graph Algorithms and Pathfinding Chapter 5: Shortest Path Algorithms 99-122 5.1 Dijkstra’s Algorithm 5.2 Bellman–Ford Algorithm 5.3 Floyd–Warshall Algorithm 5.4 Johnson’s Algorithm 5.5 Applications in Robotics, Navigation, AI Planning ________________________________________ Chapter 6: Advanced Pathfinding in AI 123-151 6.1 Introduction to AI Pathfinding 6.2 A* Search Algorithm 6.3 Heuristics and Admissibility 6.4 Iterative Deepening A* (IDA*) 6.5 Jump Point Search 6.6 Pathfinding in Games and Autonomous Systems ________________________________________ Chapter 7: Minimum Spanning Trees 152-179 7.1 Kruskal’s Algorithm 7.2 Prim’s Algorithm 7.3 Cycle Detection with DSU 7.4 Applications in Network Design & Clustering ________________________________________ Chapter 8: Network Flows and Cuts 180-207 8.1 Max Flow–Min Cut Theorem 8.2 Ford-Fulkerson Algorithm 8.3 Edmonds–Karp Algorithm 8.4 Applications in Scheduling, Matching & AI Resource Allocation ________________________________________ Part III: Social Network Analysis with Graph Theory Chapter 9: Social Networks and Graph Structures 208-238 9.1 Graph-Based Modeling of Social Interaction 9.2 Homophily and Influence 9.3 Small-World Phenomenon 9.4 Community Structures ________________________________________ Chapter 10: Centrality Measures in Social Networks 239-257 10.1 Degree Centrality 10.2 Betweenness Centrality 10.3 Closeness Centrality 10.4 Eigenvector & PageRank 10.5 Applications in AI-driven Influence Prediction ________________________________________ Chapter 11: Community Detection Algorithms 258-278 11.1 Modularity Optimization 11.2 Girvan–Newman Algorithm 11.3 Spectral Clustering 11.4 Label Propagation 11.5 Social Recommendation & AI Applications ________________________________________ Chapter 12: Link Prediction & Graph Mining 279-301 12.1 Similarity-Based Methods 12.2 Probabilistic Models 12.3 Matrix Factorization 12.4 Graph Embeddings for Link Prediction 12.5 Applications: Fraud Detection, Friend Suggestion ________________________________________

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