📋 Executive Summary

Document: Graph Algorithms
Type: Technical Documentation
Reading Time: ~15 min
Last Updated: December 2025

📊 Quick Stats

🎯 Main Topics Covered

1. Graph Representations — Adjacency matrix vs adjacency list trade-offs
2. BFS & DFS — Traversal algorithms and their applications
3. Shortest Path Algorithms — Dijkstra’s, Bellman-Ford, Floyd-Warshall
4. Minimum Spanning Trees — Kruskal’s and Prim’s algorithms
5. Topological Sorting — DFS and Kahn’s algorithm
6. Cycle Detection — In directed and undirected graphs
7. Connected Components — Finding and counting components
8. Advanced Topics — Tarjan’s SCC, articulation points, bridges

💡 What You’ll Learn

• Choose optimal graph representation for different problem types
• Apply BFS for shortest path in unweighted graphs
• Use DFS for cycle detection and topological sorting
• Implement Dijkstra’s algorithm for weighted shortest paths
• Build minimum spanning trees for network design problems
• Detect cycles in both directed and undirected graphs
• Find strongly connected components using Tarjan’s/Kosaraju’s
• Solve dependency resolution with topological sorting

📚 Prerequisites

• Solid understanding of arrays and linked lists
• Familiarity with recursion and stack operations
• Knowledge of queues for BFS implementation
• Basic understanding of tree traversals
• Big-O notation and complexity analysis

👥 Target Audience

✅ CS Students — Learning graph theory and algorithms
✅ Interview Candidates — Mastering graph questions for coding interviews
✅ Backend Engineers — Working with network/relationship data
✅ System Designers — Building dependency systems and routing

🎓 Learning Path

Beginner → Graph representations, BFS/DFS basics
Intermediate → Shortest paths, MST, topological sort
Advanced → Strongly connected components, articulation points

Graphs

Traversal, shortest paths, MST, topology.