# etour

##### Constructs eulerian tours on a graph.

`etour`

-- Constructs an eulerian tour on a graph using Hierholzer's algorithm. Returns a vector of node labels. If `weighted`

is `TRUE`

constructs a weight-decreasing eulerian using the modified Hierholzer's algorithm. Usually `etour`

is not called directly, rather the generic function `eulerian`

is used.

- Keywords
- graphs

##### Usage

`etour(g, start=NULL,weighted=TRUE)`

##### Arguments

- g
a graph satisfying

`is_even_graph`

- start
an optional starting node for the tour.

- weighted
whether tour uses weights

##### Details

The supplied graph should satisfy`is_even_graph`

. If `weighted`

is `TRUE`

the lowest weight edge is found, and the tour starts at the
one of its nodes, picking the node with the bigger second-smallest edge weight.
After that the tour follows weight-increasing edges.
If `weighted`

is `FALSE`

weights are ignored. The returned tour is typically a closed path. However, if the last edge is a duplicated edge added to make the graph even, this edge is omitted and the result is an open path.

##### References

see overview

##### Examples

```
# NOT RUN {
require(PairViz)
g <- mk_even_graph(5)
etour(g)
g <- mk_even_graph(6) # adds 3 extra edges to g, so all nodes are even
etour(g)
etour(g, start= "4") # modifies the starting node
eulerian(6) # The eulerian wrapper looks after making even graph,
#also returns numbers rather than nodes
# On a general graph.
v <- LETTERS[1:4]
g <- new("graphNEL",nodes=v)
g <- addEdge(v[1],v[3:4],g,1:2)
g <- addEdge(v[2],v[3:4],g,3:4)
etour(g)
eulerian(g) # Equivalently, use eulerian wrapper
n <- LETTERS[1:5]
g <- new("graphNEL",nodes=n)
g <- addEdge(n[1],n[2:3],g)
g <-addEdge(n[2],n[3:5],g)
g <-addEdge(n[4],n[3],g)
is_even_graph(g)
etour(mk_even_graph(g))
eulerian(g) # Equivalently, use eulerian wrapper
# }
```

*Documentation reproduced from package PairViz, version 1.3.2, License: GPL-2*