Graph Theory Playground Math

What is the Graph Theory Playground?

Quick Answer: An interactive tool to build and explore graphs. Add nodes, connect them with weighted edges, and run Dijkstra's algorithm to find the shortest path from a selected source node to all others. Distances and the shortest-path tree are highlighted visually.

Theory of Graphs and Dijkstra's Algorithm

A graph consists of vertices (nodes) and edges (connections) that may have weights. Dijkstra's algorithm finds the shortest path from a source node to all other nodes in a graph with non‑negative edge weights. It maintains a set of visited nodes and repeatedly selects the unvisited node with the smallest tentative distance, updating neighbors. This playground lets you create a graph by clicking, then see the algorithm in action: the shortest path tree edges turn green, and distances are displayed on nodes.

Step-by-Step Examples

Example 1: Simple Shortest Path

1. Click "Add Node Mode" and click on the canvas to place 4-5 nodes.
2. Switch to "Connect Mode". Click on one node, then another to create a weighted edge (random weight 1-10). Build a small network.
3. Click "Select Source", then click a node to set it as the start.
4. Click "Run Dijkstra". The shortest distances appear on nodes, and the edges forming the shortest path tree are highlighted in green.

Example 2: Unweighted Graph (BFS)

1. Create edges but set all weights to 1 (manually edit? No, they are random. But for unweighted, you can imagine all weights=1; Dijkstra still works as BFS).
2. Run Dijkstra; the algorithm will find the path with fewest edges if weights are equal.

Frequently Asked Questions