mst.py

import numpy as np
from scipy.spatial.distance import pdist, squareform
import matplotlib.pyplot as plt
 
 
def minimum_spanning_tree(X, copy_X=True):
    """X are edge weights of fully connected graph"""
    if copy_X:
        X = X.copy()
 
    if X.shape[0] != X.shape[1]:
        raise ValueError("X needs to be square matrix of edge weights")
    n_vertices = X.shape[0]
    spanning_edges = []
     
    # initialize with node 0:                                                                                         
    visited_vertices = [0]                                                                                            
    num_visited = 1
    # exclude self connections:
    diag_indices = np.arange(n_vertices)
    X[diag_indices, diag_indices] = np.inf
     
    while num_visited != n_vertices:
        new_edge = np.argmin(X[visited_vertices], axis=None)
        # 2d encoding of new_edge from flat, get correct indices                                                      
        new_edge = divmod(new_edge, n_vertices)
        new_edge = [visited_vertices[new_edge[0]], new_edge[1]]                                                       
        # add edge to tree
        spanning_edges.append(new_edge)
        visited_vertices.append(new_edge[1])
        # remove all edges inside current tree
        X[visited_vertices, new_edge[1]] = np.inf
        X[new_edge[1], visited_vertices] = np.inf                                                                     
        num_visited += 1
    return np.vstack(spanning_edges)
 
 
def test_mst():
    P = np.random.uniform(size=(50, 2))
    print P
 
    X = squareform(pdist(P))
    edge_list = minimum_spanning_tree(X)
    plt.scatter(P[:, 0], P[:, 1])
     
    for edge in edge_list:
        i, j = edge
        plt.plot([P[i, 0], P[j, 0]], [P[i, 1], P[j, 1]], c='r')
    plt.show()
 
if __name__ == "__main__":
    test_mst()