Use this if you are using igraph from R
A subgraph of a connected graph is a minimum spanning tree if it is tree, and the sum of its edge weights are the minimal among all tree subgraphs of the graph. A minimum spanning forest of a graph is the graph consisting of the minimum spanning trees of its components.
mst(graph, weights = NULL, algorithm = NULL, ...)
graph 
The graph object to analyze. 
weights 
Numeric algorithm giving the weights of the edges in the
graph. The order is determined by the edge ids. This is ignored if the

algorithm 
The algorithm to use for calculation. 
... 
Additional arguments, unused. 
If the graph is unconnected a minimum spanning forest is returned.
A graph object with the minimum spanning forest. (To check that it
is a tree check that the number of its edges is vcount(graph)1
.)
The edge and vertex attributes of the original graph are preserved in the
result.
Gabor Csardi csardi.gabor@gmail.com
Prim, R.C. 1957. Shortest connection networks and some generalizations Bell System Technical Journal, 37 1389–1401.
g < sample_gnp(100, 3/100) g_mst < mst(g)