There are a number of algorithms that have been proposed in graph theory literature to compute the minimum spanning tree of a given graph. These include the famous Prim’s and Kruskal’s algorithm, among others. The main drawback of these algorithms is their greedy nature, which means they cannot be applied to large datasets. It uses K-means to find the MST with a reduced complexity of O(N 1.5 ).

The steps of making the MST are as follows:
aMST_one:

• Making clusters(1) of the data points
• Running an MST algorithm on each of the clusters formed forming subset MSTs for each cluster(2)
• Making a separate MST(3) of the centroids of the clusters
• On adjacent centroid MST edges of (3), joining the subset MSTs in (2) according to the closest point of the adjacent centroid MSTs
  
  aMST_two:
• Making clusters(a) considering centroids as - the midpoints of adjacent centorids MST edges of (3)
• Running an MST algorithm on each of the clusters formed forming subset MSTs for each cluster(b)
• Making a separate MST(c) of the centroids of the clusters
• On adjacent centroid MST edges of (c), joining the subset MSTs in (b) according to the closest point of the adjacent centroid MSTs

• Combine edges of aMST_one and aMST_two to form a graph
• Run an MST algorithm on this graph

The code was tested on Python 2.7.11.