Mastering Graph Algorithms Course Syllabus

Overview: This course provides a comprehensive, code-first exploration of graph algorithms, blending theoretical foundations with hands-on implementation. Designed for learners with a programming background, it spans approximately 12.5 hours of active learning, structured into eight modules. You'll progress from core graph representations to advanced algorithms and real-world applications, culminating in a capstone project that synthesizes your skills into a deployable graph-analysis tool. Each module combines clear explanations with practical coding exercises, preparing you to solve complex problems in routing, recommendation, and network design.

Module 1: Graph Fundamentals & Representations

Estimated time: 1 hours

• Understand graph definitions and terminology
• Differentiate between directed and undirected graphs
• Compare weighted vs. unweighted graphs
• Implement adjacency list and matrix representations

Module 2: Breadth-First & Depth-First Search

Estimated time: 1.5 hours

• Implement BFS for shortest unweighted paths
• Apply DFS for connectivity and backtracking
• Use DFS for cycle detection in graphs
• Perform topological sorting using DFS

Module 3: Shortest Path Algorithms

Estimated time: 2 hours

• Implement Dijkstra’s algorithm using priority queues
• Apply Bellman–Ford for graphs with negative edge weights
• Use A* heuristic for pathfinding optimization
• Compare performance on road-network data

Module 4: Minimum Spanning Trees

Estimated time: 1.5 hours

• Understand greedy strategies for MSTs
• Implement Kruskal’s algorithm with Union-Find
• Build MSTs using Prim’s algorithm with heaps

Module 5: Network Flow & Matching

Estimated time: 2 hours

• Apply the max-flow/min-cut theorem
• Implement Ford–Fulkerson and Edmonds–Karp algorithms
• Solve bipartite matching via flow reduction

Module 6: Advanced Topics & Applications

Estimated time: 1.5 hours

• Analyze graph coloring for scheduling
• Detect strongly connected components using Kosaraju’s and Tarjan’s algorithms
• Explore planarity and graph embeddings

Module 7: Real-World Case Studies

Estimated time: 1 hours

• Build a friend-recommendation engine
• Prototype a shortest-route planner
• Apply graph algorithms to influence maximization

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

Estimated time: 2 hours

• Select and model a real-world problem as a graph
• Choose and implement appropriate algorithms
• Visualize results and optimize for performance

Prerequisites

• Proficiency in a programming language (Python, Java, or C++)
• Familiarity with basic data structures (arrays, queues, heaps)
• Understanding of time and space complexity analysis

What You'll Be Able to Do After

• Model real-world systems as graph structures
• Implement and compare core graph traversal algorithms
• Compute shortest paths and minimum spanning trees efficiently
• Solve network flow and bipartite matching problems
• Build and deploy a full-featured graph analysis tool