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📋 Executive Summary

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

📊 Quick Stats

Metric Value
Core Algorithms 12+ essential techniques
Representations 2 methods (Adjacency Matrix/List)
Traversals BFS & DFS with variations
Shortest Path 4 algorithms (Dijkstra, Bellman-Ford, Floyd-Warshall, A*)
Practice Problems 25+ curated questions

🎯 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.