getMinimumCutTree: getMinimumCutTree ————– Computes a minimum cut tree
In optrees: Optimal Trees in Weighted Graphs

Description Usage Arguments Details Value References Examples

Given a connected weighted undirected graph, getMinimumCutTree computes a minimum cut tree, also called Gomory-Hu tree. This function uses the Gusfield's algorithm to find it.

1 2	getMinimumCutTree(nodes, arcs, algorithm = "Gusfield", show.data = TRUE, show.graph = TRUE, check.graph = FALSE)

`nodes`	vector containing the nodes of the graph, identified by a number that goes from 1 to the order of the graph.
`arcs`	matrix with the list of arcs of the graph. Each row represents one arc. The first two columns contain the two endpoints of each arc and the third column contains their weights.
`algorithm`	denotes the algorithm to use for find a minimum cut tree or Gomory-Hu tree: "Gusfield".
`check.graph`	logical value indicating if it is necesary to check the graph. Is `FALSE` by default.
`show.data`	logical value indicating if the function displays the console output (`TRUE`) or not (`FALSE`). The default is `TRUE`.
`show.graph`	logical value indicating if the function displays a graphical representation of the graph and its minimum cut tree (`TRUE`) or not (`FALSE`). The default is `TRUE`.

The minimum cut tree or Gomory-Hu tree was introduced by R. E. Gomory and T. C. Hu in 1961. Given a connected weighted undirected graph, the Gomory-Hu tree is a weighted tree that contains the minimum s-t cuts for all s-t pairs of nodes in the graph. Gomory and Hu developed an algorithm to find this tree, but it involves maximum flow searchs and nodes contractions.

In 1990, Dan Gusfield proposed a new algorithm that can be used to find the Gomory-Hu tree without any nodes contraction and simplifies the implementation.

getMinimumCutTree returns a list with:

`tree.nodes`	vector containing the nodes of the minimum cut tree.
`tree.arcs`	matrix containing the list of arcs of the minimum cut tree.
`weight`	value with the sum of weights of the arcs.
`stages`	number of stages required.
`time`	time needed to find the minimum cut tree.

This function also represents the graph and the minimum cut tree and prints in console the results whit additional information (number of stages, computational time, etc.).

R. E. Gomory, T. C. Hu. Multi-terminal network flows. Journal of the Society for Industrial and Applied Mathematics, vol. 9, 1961.

Dan Gusfield (1990). "Very Simple Methods for All Pairs Network Flow Analysis". SIAM J. Comput. 19 (1): 143-155.

# Graph
nodes <- 1:6
arcs <- matrix(c(1,2,1, 1,3,7, 2,3,1, 2,4,3, 2,5,2, 3,5,4, 4,5,1, 4,6,6,
                5,6,2), byrow = TRUE, ncol = 3)
# Minimum cut tree
getMinimumCutTree(nodes, arcs)