# mstBird

From cooptrees v1.0
by Manuel Fontenla

##### Bird rule for minimum cost spanning tree problems

Given a graph with at least one minimum cost spanning tree,
the `mstBird`

function divides the cost of the tree
obtained with Prim's algorithm among the agents. For that
purpose it uses the Bird rule, where each agent pays the
cost of the arc that connects him to the tree source.

##### Usage

`mstBird(nodes, arcs)`

##### Arguments

- 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.

##### Value

`mstBird`

returns a matrix with the agents and their
costs.
##### See Also

The more general function mstRules.

##### Examples

```
# Graphs
nodes <- 1:4
arcs <- matrix(c(1,2,6, 1,3,10, 1,4,6, 2,3,4, 2,4,6, 3,4,4),
byrow = TRUE, ncol = 3)
# Bird
mstBird(nodes, arcs)
```

*Documentation reproduced from package cooptrees, version 1.0, License: GPL-3*

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