2 min read
📋 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
- Graph Representations — Adjacency matrix vs adjacency list trade-offs
- BFS & DFS — Traversal algorithms and their applications
- Shortest Path Algorithms — Dijkstra’s, Bellman-Ford, Floyd-Warshall
- Minimum Spanning Trees — Kruskal’s and Prim’s algorithms
- Topological Sorting — DFS and Kahn’s algorithm
- Cycle Detection — In directed and undirected graphs
- Connected Components — Finding and counting components
- 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.