A spanning tree of a connected graph is a connected subgraph with the smallest number of edges that includes all vertices of the graph. A graph will have many spanning trees. Among these, the minimum spanning tree will have the smallest sum of edge weights.
mst(graph, weights = NULL, algorithm = NULL, ...)The graph object to analyze.
Numeric vector giving the weights of the edges in the
graph. The order is determined by the edge ids. This is ignored if the
unweighted algorithm is chosen. Edge weights are interpreted as
distances.
The algorithm to use for calculation. unweighted can
be used for unweighted graphs, and prim runs Prim's algorithm for
weighted graphs. If this is NULL then igraph will select the
algorithm automatically: if the graph has an edge attribute called
weight or the weights argument is not NULL then Prim's
algorithm is chosen, otherwise the unweighted algorithm is used.
Additional arguments, unused.
A graph object with the minimum spanning forest. To check whether 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.
The minimum spanning forest of a disconnected graph is the collection of minimum spanning trees of all of its components.
If the graph is not connected a minimum spanning forest is returned.
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)