Boruvka's Algorithm

An implementation of Boruvka's algorithm to find a minimum spanning tree in a graph.

Link to narrated video demonstration on YouTube.

Example

stdout (Terminal Output)

Finding MST with Boruvka's algorithm:
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8]
Edges (node1, node2, weight):
    (0, 1, 4)
    (0, 6, 7)
    (1, 2, 9)
    (1, 6, 11)
    (1, 7, 20)
    (2, 3, 6)
    (2, 4, 2)
    (3, 4, 10)
    (3, 5, 5)
    (4, 5, 15)
    (4, 7, 1)
    (4, 8, 5)
    (5, 8, 12)
    (6, 7, 1)
    (7, 8, 3)

Iteration 1:
Current MST edges: []
Current MST Weight: 0
Added edge 0 - 1 with weight 4 to MST.
Added edge 2 - 4 with weight 2 to MST.
Added edge 3 - 5 with weight 5 to MST.
Added edge 4 - 7 with weight 1 to MST.
Added edge 6 - 7 with weight 1 to MST.
Added edge 7 - 8 with weight 3 to MST.

Iteration 2:
Current MST edges: [(0, 1, 4), (2, 4, 2), (3, 5, 5), (4, 7, 1), (6, 7, 1), (7, 8, 3)]
Current MST Weight: 16
Added edge 0 - 6 with weight 7 to MST.
Added edge 2 - 3 with weight 6 to MST.

MST found with Boruvka's algorithm.
MST edges (node1, node2, weight):
    (0, 1, 4)
    (0, 6, 7)
    (2, 3, 6)
    (2, 4, 2)
    (3, 5, 5)
    (4, 7, 1)
    (6, 7, 1)
    (7, 8, 3)
MST weight: 29

Usage

Installing Dependencies

Install uv if you haven't already.

Run the following command from the project root directory:

uv sync --dev

Running the Application

Run the following command from the project root directory:

uv run python -m src.boruvkas_algorithm.boruvka

Running Tests

Run the following command from the project root directory:

uv run pytest -v