Query and manipulate a graph as it were an adjacency matrix

## Usage

``````# S3 method for class 'igraph'
`[`(
x,
i,
j,
...,
from,
to,
sparse = igraph_opt("sparsematrices"),
edges = FALSE,
drop = TRUE,
attr = if (is_weighted(x)) "weight" else NULL
)``````

## Arguments

x

The graph.

i

Index. Vertex ids or names or logical vectors. See details below.

j

Index. Vertex ids or names or logical vectors. See details below.

...

Currently ignored.

from

A numeric or character vector giving vertex ids or names. Together with the `to` argument, it can be used to query/set a sequence of edges. See details below. This argument cannot be present together with any of the `i` and `j` arguments and if it is present, then the `to` argument must be present as well.

to

A numeric or character vector giving vertex ids or names. Together with the `from` argument, it can be used to query/set a sequence of edges. See details below. This argument cannot be present together with any of the `i` and `j` arguments and if it is present, then the `from` argument must be present as well.

sparse

Logical scalar, whether to return sparse matrices.

edges

Logical scalar, whether to return edge ids.

drop

Ignored.

attr

If not `NULL`, then it should be the name of an edge attribute. This attribute is queried and returned.

## Value

A scalar or matrix. See details below.

## Details

The single bracket indexes the (possibly weighted) adjacency matrix of the graph. Here is what you can do with it:

1. Check whether there is an edge between two vertices (\(v\) and \(w\)) in the graph:

``  graph[v, w]``

A numeric scalar is returned, one if the edge exists, zero otherwise.

2. Extract the (sparse) adjacency matrix of the graph, or part of it:

``````  graph[]
graph[1:3,5:6]
graph[c(1,3,5),]``````

The first variants returns the full adjacency matrix, the other two return part of it.

3. The `from` and `to` arguments can be used to check the existence of many edges. In this case, both `from` and `to` must be present and they must have the same length. They must contain vertex ids or names. A numeric vector is returned, of the same length as `from` and `to`, it contains ones for existing edges edges and zeros for non-existing ones. Example:

``  graph[from=1:3, to=c(2,3,5)]``

.

4. For weighted graphs, the `[` operator returns the edge weights. For non-esistent edges zero weights are returned. Other edge attributes can be queried as well, by giving the `attr` argument.

5. Querying edge ids instead of the existance of edges or edge attributes. E.g.

``  graph[1, 2, edges=TRUE]``

returns the id of the edge between vertices 1 and 2, or zero if there is no such edge.

6. Adding one or more edges to a graph. For this the element(s) of the imaginary adjacency matrix must be set to a non-zero numeric value (or `TRUE`):

``````  graph[1, 2] <- 1
graph[1:3,1] <- 1
graph[from=1:3, to=c(2,3,5)] <- TRUE``````

This does not affect edges that are already present in the graph, i.e. no multiple edges are created.

7. Adding weighted edges to a graph. The `attr` argument contains the name of the edge attribute to set, so it does not have to be ‘weight’:

``````  graph[1, 2, attr="weight"]<- 5
graph[from=1:3, to=c(2,3,5)] <- c(1,-1,4)``````

If an edge is already present in the network, then only its weights or other attribute are updated. If the graph is already weighted, then the `attr="weight"` setting is implicit, and one does not need to give it explicitly.

8. Deleting edges. The replacement syntax allow the deletion of edges, by specifying `FALSE` or `NULL` as the replacement value:

``  graph[v, w] <- FALSE``

removes the edge from vertex \(v\) to vertex \(w\). As this can be used to delete edges between two sets of vertices, either pairwise:

``  graph[from=v, to=w] <- FALSE``

or not:

``  graph[v, w] <- FALSE ``

if \(v\) and \(w\) are vectors of edge ids or names.

`[`’ allows logical indices and negative indices as well, with the usual R semantics. E.g.

``  graph[degree(graph)==0, 1] <- 1``

adds an edge from every isolate vertex to vertex one, and

``````  G <- make_empty_graph(10)
G[-1,1] <- TRUE``````

creates a star graph.

Of course, the indexing operators support vertex names, so instead of a numeric vertex id a vertex can also be given to ‘`[`’ and ‘`[[`’.

Other structural queries: `[[.igraph()`, `adjacent_vertices()`, `are_adjacent()`, `ends()`, `get.edge.ids()`, `gorder()`, `gsize()`, `head_of()`, `incident()`, `incident_edges()`, `is_directed()`, `neighbors()`, `tail_of()`