Minimum Spanning Tree Visualizer

Explore Kruskal's and Prim's algorithms with interactive weighted graph visualization

Graph Setup

Algorithm Controls

Graph Visualization

Nodes

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Edges

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MST Edges

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Total MST Weight

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MST Edges

No MST computed yet. Select an algorithm and click "Start Algorithm".

Help

What is a Minimum Spanning Tree?
  • Minimum Spanning Tree (MST): A subset of edges that connects all nodes with minimum total weight
  • Contains exactly (V-1) edges for V nodes
  • No cycles - forms a tree structure
  • Minimizes the sum of all edge weights
  • Used in network design, clustering, and optimization problems
Algorithms
  • Kruskal's Algorithm: Sorts edges by weight and adds them if they don't create a cycle
  • Uses Union-Find data structure for cycle detection
  • Time complexity: O(E log E) where E is the number of edges
  • Works on the entire graph at once
  • Prim's Algorithm: Grows the MST from a starting node
  • Always adds the minimum weight edge connecting MST to a new node
  • Time complexity: O(E log V) with binary heap
  • Requires selecting a start node
How to Use
  • Add nodes by entering labels (A, B, C, etc.)
  • Connect nodes by selecting two nodes, entering a weight, and clicking Add Edge
  • All edges are undirected (bidirectional)
  • Select Kruskal's (works on all edges) or Prim's (needs a start node)
  • Use Start to animate or Step to advance manually
  • MST edges are highlighted in green with thicker lines
  • Current edge being considered is shown in yellow
  • Generate sample graphs to see the algorithms in action
Visualization Colors
  • Gray: Unprocessed edges
  • Yellow: Current edge being evaluated
  • Green: Edges included in the MST
  • Red: Edges rejected (would create a cycle in Kruskal's)
  • Light Blue: Nodes in the MST (Prim's algorithm)