Graph Theory Path Finder | Dijkstra & A* Algorithm Visualizer

GRAPH THEORY SHORTEST PATH FINDER

Dijkstra · A* Search · Dynamic Visualizer

Graph Theory

Click canvas to add nodes, drag to move them, or drag between nodes to create weighted edges. Select an algorithm and start/end nodes to calculate the shortest path.

Algorithm: Dijkstra's Algorithm A* Search Algorithm (Euclidean Heuristic)

Start Node:

End Node:

Path Computation & Metrics

Total Path Weight 0

Hops / Edges 0

Nodes Visited 0

Path Status -

Optimal Path Sequence None

Interactive Graph Canvas

Graph Theory & Shortest Path Algorithms

Graph Theory studies network structures composed of nodes (vertices) connected by links (edges). Shortest path algorithms determine the minimum cumulative edge weight required to traverse between a source node and a target destination.

1. Algorithm Comparison

Algorithm	Time Complexity	Heuristic Search	Primary Use Case
Dijkstra's Algorithm	$$\mathcal{O}((V + E) \log V)$$	No (Uniform Cost)	Guaranteed shortest path in weighted graphs with non-negative edges.
A* Search	$$\mathcal{O}(E)$$ (Best) / $$\mathcal{O}(V^2)$$	Yes (Euclidean/Manhattan)	Heuristic-guided spatial pathfinding (video games, GIS routing).
Bellman-Ford	$$\mathcal{O}(V \cdot E)$$	No	Graphs with negative edge weights or negative cycle detection.

2. Key Graph Concepts

• Adjacency Matrix & List: Fundamental data structures used to encode vertex relationships and edge weights.
• Admissible Heuristic: In A* search, a heuristic function $h(n)$ is admissible if it never overestimates the actual cost to reach the goal.

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