igraph (version 0.7.1)

iterators: Vertex and edge sequences and iterators

Description

Vertex and edge sequences are central concepts of igraph.

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 $ operator to select (or modify) the attributes of a subset of vertices. A vertex sequence can be indexed by a logical expression, and this expression may contain the names of the vertex attributes and ordinary variables as well. The return value of such a construct (ie. a vertex sequence indexed by a logical expression) is another vertex sequence containing only vertices from the original sequence for which the expression evaluates to TRUE.

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 graph. Edge sequences can be also indexed with logical expressions containing edge attributes: g <- graph.ring(10) E(g)$weight <- runif(ecount(g)) E(g)$width <- 1 E(g)[ weight >= 0.5 ]$width <- 3 plot(g, layout=layout.circle, edge.width=E(g)$width, edge.color="black")

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 incoming neighbors (nei(v, mode="in")), and outnei(v) is a shorthand for the outgoing neighbors (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.

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))