Mastering Graph Algorithms Course

Module 1: Graph Fundamentals & Representations

1 hour

• Topics: Definitions, directed vs. undirected, weighted vs. unweighted, adjacency structures

• Hands-on: Implement and compare adjacency list and matrix representations

Module 2: Breadth-First & Depth-First Search

1.5 hours

• Topics: BFS for shortest unweighted paths, DFS for connectivity, cycle detection, and backtracking

• Hands-on: Code BFS/DFS routines; apply DFS to find connected components and topological sort

Module 3: Shortest Path Algorithms

2 hours

• Topics: Dijkstra’s algorithm with priority queues, Bellman–Ford for negative edges, A* heuristics

• Hands-on: Implement each algorithm; compare performance on sample road-network data

Module 4: Minimum Spanning Trees

1.5 hours

• Topics: Greedy strategies, Kruskal’s with Union-Find, Prim’s with heaps

• Hands-on: Build MSTs for weighted graphs and visualize resulting tree structures

Module 5: Network Flow & Matching

2 hours

• Topics: Max-flow/min-cut theorem, Ford–Fulkerson, Edmonds–Karp, bipartite matching via flow reduction

• Hands-on: Solve flow problems on capacity graphs and implement bipartite matching

Module 6: Advanced Topics & Applications

1.5 hours

• Topics: Graph coloring, strongly connected components (Kosaraju’s/Tarjan’s), planarity and embeddings

• Hands-on: Detect SCCs in directed graphs; apply graph coloring to scheduling problems

Module 7: Real-World Case Studies

1 hour

• Topics: Recommendation systems via graph algorithms, influence maximization, route optimization

• Hands-on: Prototype a simple friend-recommendation engine and a shortest-route planner

Module 8: Capstone Project – End-to-End Graph Solver

2 hours

• Topics: Problem selection, algorithm choice, performance tuning, and scalability considerations

• Hands-on: Build a full-featured graph-analysis tool that ingests dataset, runs selected algorithms, and visualizes results

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