# iterators

##### Vertex and edge sequences and iterators

Vertex and edge sequences are central concepts of igraph.

- Keywords
- graphs

##### Usage

```
V(graph)
E(graph, P=NULL, path=NULL, directed=TRUE)
```

##### Arguments

- graph
- A graph object.
- P
- Numeric vector for selecting edges by giving their end points. See details below.
- path
- Numeric vector, this is for selecting all edges along a path. See also details below.
- directed
- Logcal constant, can be supplied only if either
`P`

or`path`

is also present and gives whether the pairs or the path are directed or not.

##### Details

One often needs to perform an operation on a subset of vertices of edges in a graph.

A vertex sequence is simply a vector containing vertex ids, but it has a special class attribute which makes it possible to perform graph specific operations on it, like selecting a subset of the vertices based on some vertex attributes.

A vertex sequence is created by `V(g)`

this selects are vertices
in increasing vertex id order. A vertex sequence can be indexed by a
numeric vector, and a subset of all vertices can be
selected.

Vertex sequences provide powerful operations for dealing with vertex
attributes. A vertex sequence can be indexed with the
`$`

Let us see an example to make everything clear. We assign random numbers between 1 and 100 to the vertices, and select those vertices for which the number is less than 50. We set the color of these vertices to red. g <- graph.ring(10) V(g)$number <- sample(1:100, vcount(g), replace=TRUE) V(g)$color <- "grey" V(g)[ number < 50 ]$color <- "red" plot(g, layout=layout.circle, vertex.color=V(g)$color, vertex.label=V(g)$number)

There is a similar notation for edges. `E(g)`

selects all edges
from the `g`

It is important to note that, whenever we use iterators to assign new attribute values, the new values are recycled. So in the following example half of the vertices will be black, the other half red, in an alternated way. g <- graph.ring(10) V(g)$color <- c("black", "red") plot(g, layout=layout.circle)

For the recycling, the standard R rules apply and a warning is given
if the number of items to replace is not a multiple of the replacement
length. E.g. the following code gives a warning, because we set the
attribute for three vertices, but supply only two values:
g <- graph.tree(10)
V(g)$color <- "grey"
V(g)[1:3]$color <- c("green", "blue")
If a new vertex/edge attribute is created with an assignment, but only
a subset of of vertices are specified, then the rest is set to
`NA`

if the new values are in a vector and to `NULL`

if they
are a list. Try the following:
V(g)[5]$foo <- "foo"
V(g)$foo
V(g)[5]$bar <- list(bar="bar")
V(g)$bar
There are some special functions which are only defined in the
indexing expressions of vertex and edge sequences. For vertex
sequences these are: `nei`

, `inc`

, `from`

and
`to`

, `innei`

and `outnei`

. (The `adj`

special
function is an alias for `inc`

, for compatibility reasons.)

`nei`

has a mandatory and an optional argument, the first is
another vertex sequence, the second is a mode argument similar to that
of the `neighbors`

function. `nei`

returns a logical
vector of the same length as the indexed vertex sequence and evaluates
to `TRUE`

for those vertices only which have a neighbor vertex in
the vertex sequence supplied as a parameter. Thus for selecting all
neighbors of vertices 1 and 2 one can write:
V(g) [ nei( 1:2 ) ]
The mode argument (just like for `neighbors`

) gives the
type of the neighbors to be included, it is interpreted only in
directed graphs, and defaults to all types of neighbors. See the
example below. `innei(v)`

is a shorthand for the `nei(v, mode="in")`

), and `outnei(v)`

is a
shorthand for the `nei(v,mode="out")`

).

`inc`

takes an edge sequence as an argument and returns
`TRUE`

for vertices which have at least one incident edge in it.

`from`

and `to`

are similar to `inc`

but only edges
originated at (`from`

) or pointing to (`to`

) are taken into
account.

For edge sequences the special functions are: `inc`

, `from`

,
`to`

, `%--%`

, `%->%`

and `%<-%`

.

`inc`

takes a vertex sequence as an argument and returns
`TRUE`

for edges which have an incident vertex in it.

`from`

and `to`

are similar to `inc`

, but only vertices
at the source (`from`

) or target (`to`

) of the edge.

The `%--%`

operator selects edges connecting two vertex
sequences, the direction of the edges is ignored. The `%->%`

is
different only for directed graphs and only edges pointing from the
left hand side argument to the right hand side argument are selected.
`%<-%`

is exactly the opposite, it selects edges pointing from
the right hand side to the left hand side.

`E`

has two optional arguments: `P`

and `path`

. If
given `P`

can be used to select edges based on their end points,
eg. `E(g, P=c(1,2))`

selects edge `1->2`

.

`path`

can be used to select all edges along a path. The path
should be given with the visited vertex ids in the appropriate order.
See also the examples below.

##### Note

A note about the performance of the `V`

and `E`

functions,
and the selection of edges and vertices. Since all selectors
are evaluated as logical vectors on all vertices/edges, their
performance is bad on large graphs. (Time complexity is proportional
to the total number of vertices/edges.) We suggest using the
`neighbors`

, `incident`

functions and
simple R vector operations for manipulating vertex/edge sequences
in large graphs.

##### Examples

```
# mean degree of vertices in the largest cluster in a random graph
g <- erdos.renyi.game(100, 2/100)
c <- clusters(g)
vsl <- which(which.max(c$csize)==c$membership)
mean(degree(g, vsl))
# set the color of these vertices to red, others greens
V(g)$color <- "green"
V(g)[vsl]$color <- "red"
plot(g, vertex.size=3, labels=NA, vertex.color="a:color",
layout=layout.fruchterman.reingold)
# the longest geodesic within the largest cluster
long <- numeric()
for (v in vsl) {
paths <- get.shortest.paths(g, from=v, to=vsl)
fl <- paths[[ which.max(sapply(paths, length)) ]]
if (length(fl) > length(long)) {
long <- fl
}
}
# the mode argument of the nei() function
g <- graph( c(1,2, 2,3, 2,4, 4,2) )
V(g)[ nei( c(2,4) ) ]
V(g)[ nei( c(2,4), "in") ]
V(g)[ nei( c(2,4), "out") ]
# operators for edge sequences
g <- barabasi.game(100, power=0.3)
E(g) [ 1:3 %--% 2:6 ]
E(g) [ 1:5 %->% 1:6 ]
E(g) [ 1:3 %<-% 2:6 ]
# the edges along the diameter
g <- barabasi.game(100, directed=FALSE)
d <- get.diameter(g)
E(g, path=d)
# performance for large graphs is bad
largeg <- graph.lattice(c(1000, 100))
system.time(E(largeg)[inc(1)])
system.time(incident(largeg, 1))
```

*Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)*