Project 6: Graph Traversal Visualizer

Build a visualizer that shows BFS and DFS exploring a graph.

Project Overview

Attribute Value
Difficulty Level 2: Intermediate
Time Estimate Weekend
Main Language Python
Alternative Languages JavaScript, C++
Knowledge Area Graph theory
Tools Plotting tool or simple GUI
Main Book “Introduction to Algorithms” by Cormen et al.

What you’ll build: A tool that animates BFS and DFS on user-defined graphs and highlights visited order.

Why it teaches math: Graph traversal is the core of many algorithms, and visualization reveals structure.

Core challenges you’ll face:

  • Representing graphs as adjacency structures
  • Tracking visited nodes and traversal order
  • Rendering traversal steps clearly

Real World Outcome

You will input a graph and see BFS or DFS explore it step by step, with highlighted nodes and edges.

Example Output:

$ python traverse.py --graph sample.json --algo bfs
Visited order: A B C D E
Saved animation to bfs.gif

Verification steps:

  • Compare traversal order to expected results
  • Test on graphs with cycles and disconnected components

The Core Question You’re Answering

“How do algorithms systematically explore a network of connections?”

This project makes graph theory visible.

Concepts You Must Understand First

Stop and research these before coding:

  1. Graph representation
    • When do you use adjacency lists vs matrices?
    • Book Reference: “Introduction to Algorithms” by Cormen et al., Ch. 22
  2. Breadth-first search
    • Why does BFS find shortest paths in unweighted graphs?
    • Book Reference: “Introduction to Algorithms” by Cormen et al., Ch. 22
  3. Depth-first search
    • How does DFS uncover connected components?
    • Book Reference: “Introduction to Algorithms” by Cormen et al., Ch. 22

Questions to Guide Your Design

  1. Visualization style
    • Will you layout nodes manually or use a simple force layout?
    • How will you animate traversal steps?
  2. Traversal output
    • Will you record discovery and finishing times?
    • How will you show the queue or stack state?

Thinking Exercise

BFS vs DFS

Given a graph with nodes A-B-C and A-D-E, list the BFS and DFS orders starting at A.

Questions while working:

  • Why does BFS expand level by level?
  • How does DFS depend on edge order?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What is the difference between BFS and DFS?”
  2. “Why does BFS give shortest paths?”
  3. “How do you detect cycles in a graph?”
  4. “What is the time complexity of traversal?”
  5. “How do you represent graphs efficiently?”

Hints in Layers

Hint 1: Starting Point Start with an adjacency list representation.

Hint 2: Next Level Record traversal order and replay it in the visualizer.

Hint 3: Technical Details Track visited status to avoid infinite loops.

Hint 4: Tools/Debugging Print queue/stack state at each step to verify traversal.

Books That Will Help

Topic Book Chapter
Graph representation “Introduction to Algorithms” by Cormen et al. Ch. 22
BFS “Introduction to Algorithms” by Cormen et al. Ch. 22
DFS “Introduction to Algorithms” by Cormen et al. Ch. 22

Implementation Hints

  • Keep graph input simple (JSON or CSV).
  • Separate traversal logic from visualization.
  • Provide a static output (PNG) as a baseline before animation.

Learning Milestones

  1. First milestone: You can traverse graphs correctly.
  2. Second milestone: You can visualize traversal steps.
  3. Final milestone: You can explain BFS/DFS differences clearly.