# communities

##### Functions to deal with the result of network community detection

igraph community detection functions return their results
as an object from the `communities`

class. This manual page
describes the operations of this class.

- Keywords
- graphs

##### Usage

```
## S3 method for class 'communities':
print(x, \dots)
```## S3 method for class 'communities':
length(x)
sizes(communities)
membership(communities)
## S3 method for class 'communities':
modularity(x, \dots)
algorithm(communities)
crossing(communities, graph)

is.hierarchical(communities, full = FALSE)
merges(communities)
cutat(communities, no, steps)
## S3 method for class 'communities':
as.dendrogram(object, hang=-1,
use.modularity=FALSE, \dots)
## S3 method for class 'communities':
as.hclust(x, hang = -1,
use.modularity = FALSE, \dots)
## S3 method for class 'communities':
asPhylo(x, use.modularity=FALSE, \dots)
showtrace(communities)

code.length(communities)

## S3 method for class 'communities':
plot(x, y,
colbar=rainbow(length(x)),
col=colbar[membership(x)],
mark.groups=communities(x),
edge.color=c("black", "red")[crossing(x,y)+1],
...)

##### Arguments

- communities,x,object
- A
`communities`

object, the result of an igraph community detection function. - graph
- An igraph graph object, corresponding to
`communities`

. - full
- Logical scalar, if
`TRUE`

, then`is.hierarchical`

only returns`TRUE`

for fully hierarchical algorithms. Theleading eigenvector algorithm is hierarchical, it gives a hierarchy of groups, but not - y
- An igraph graph object, corresponding to the communities in
`x`

. - no
- Integer scalar, the desired number of communities. If too
low or two high, then an error message is given. Exactly one of
`no`

and`steps`

must be supplied. - steps
- The number of merge operations to perform to produce the
communities. Exactly one of
`no`

and`steps`

must be supplied. - colbar
- A vector of colors, in any format that is accepted by the regular R plotting methods. E.g. it may be an integer vector, a character vector of color names, a character vector of RGB colors. This vector gives the color bar for the vertices. The
- col
- A vector of colors, in any format that is accepted by the regular R plotting methods. This vector gives the colors of the vertices explicitly.
- mark.groups
- A list of numeric vectors. The communities can be
highlighted using colored polygons. The groups for which the
polygons are drawn are given here. The default is to use the groups
given by the communities. Supply
`NULL`

here if you d - edge.color
- The colors of the edges. By default the edges within communities are colored green and other edges are red.
- hang
- Numeric scalar indicating how the height of leaves should
be computed from the heights of their parents; see
`plot.hclust`

. - use.modularity
- Logical scalar, whether to use the modularity values to define the height of the branches.
- ...
- Additional arguments.
`plot.communities`

passes these to`plot.igraph`

. The other functions silently ignore them.

##### Details

Community structure detection algorithms try to find dense subgraphs in directed or undirected graphs, by optimizing some criteria, and usually using heuristics.

igraph implements a number of commmunity detection methods (see them
below), all of which return an object of the class
`communities`

. Because the community structure detection
algorithms are different, `communities`

objects do not always
have the same structure. Nevertheless, they have some common
operations, these are documented here.

The `print`

generic function is defined for `communities`

,
it prints a short summary.

The `length`

generic function call be called on
`communities`

and returns the number of communities.

The `sizes`

function returns the community sizes, in the order of
their ids.
`membership`

gives the division of the vertices, into
communities. It returns a numeric vector, one value for each vertex,
the id of its community. Community ids start from one. Note that some
algorithms calculate the complete (or incomplete) hierarchical
structure of the communities, and not just a single
partitioning. For these algorithms typically the membership for the
highest modularity value is returned, but see also the manual pages of
the individual algorithms.
`modularity`

gives the modularity score of the partitioning. (See
`modularity.igraph`

for details. For algorithms that do
not result a single partitioning, the highest modularity value is
returned.

`algorithm`

gives the name of the algorithm that was used to
calculate the community structure.

`crossing`

returns a logical vector, with one value for each
edge, ordered according to the edge ids. The value is `TRUE`

iff
the edge connects two different communities, according to the (best)
membership vector, as returned by `membership()`

.

`is.hierarchical`

checks whether a hierarchical algorithm was
used to find the community structure. Some functions only make sense
for hierarchical methods (e.g. `merges`

, `cutat`

and
`as.dendrogram`

).
`merges`

returns the merge matrix for hierarchical methods. An
error message is given, if a non-hierarchical method was used to find
the community structure. You can check this by calling
`is.hierarchical`

on the `communities`

object.

`cutat`

cuts the merge tree of a hierarchical community finding
method, at the desired place and returns a membership vector. The
desired place can be expressed as the desired number of communities or
as the number of merge steps to make. The function gives an error
message, if called with a non-hierarchical method.

`as.dendrogram`

converts a hierarchical community structure to a
`dendrogram`

object. It only works for hierarchical methods, and
gives an error message to others. See `dendrogram`

for details.

`as.hclust`

is similar to `as.dendrogram`

, but converts a
hierarchical community structure to a `hclust`

object.

`asPhylo`

converts a hierarchical community structure to
a `phylo`

object, you will need the `ape`

package for this.
`showtrace`

works (currently) only for communities found by the
leading eigenvector method
(`leading.eigenvector.community`

), and returns a character
vector that gives the steps performed by the algorithm while finding
the communities.

`code.length`

is defined for the InfoMAP method
(`infomap.community`

and returns the code length of the
partition.
It is possibly to call the `plot`

function on `communities`

objects. This will plot the graph (and uses `plot.igraph`

internally), with the communities shown. By default it colores the
vertices according to their communities, and also marks the vertex
groups corresponding to the communities. It passes additional
arguments to `plot.igraph`

, please see that and also
`igraph.plotting`

on how to change the plot.

##### Value

`print`

returns the`communities`

object itself, invisibly.`length`

returns an integer scalar.`sizes`

returns a numeric vector.`membership`

returns a numeric vector, one number for each vertex in the graph that was the input of the community detection.`modularity`

returns a numeric scalar.`algorithm`

returns a character scalar.`crossing`

returns a logical vector.`is.hierarchical`

returns a logical scalar.`merges`

returns a two-column numeric matrix.`cutat`

returns a numeric vector, the membership vector of the vertices.`as.dendrogram`

returns a`dendrogram`

object.`showtrace`

returns a character vector.`code.length`

returns a numeric scalar for communities found with the InfoMAP method and`NULL`

for other methods.`plot`

for`communities`

objects returns`NULL`

, invisibly.

##### concept

Community structure

##### See Also

See `dendPlot`

for plotting community structure
dendrograms.
See `compare.communities`

for comparing two community
structures on the same graph.
The different methods for finding communities, they all return a
`communities`

object:
`edge.betweenness.community`

,
`fastgreedy.community`

,
`label.propagation.community`

,
`leading.eigenvector.community`

,
`multilevel.community`

,
`optimal.community`

,
`spinglass.community`

,
`walktrap.community`

.

##### Examples

```
karate <- graph.famous("Zachary")
wc <- walktrap.community(karate)
modularity(wc)
membership(wc)
plot(wc, karate)
```

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