membership {igraph}

Functions to deal with the result of network community detection

Description

igraph community detection functions return their results as an object from the communities class. This manual page describes the operations of this class.

Usage

membership(communities)

## S3 method for class 'communities'
print(x, ...)

## S3 method for class 'communities'
modularity(x, ...)

## S3 method for class 'communities'
length(x)

sizes(communities)

algorithm(communities)

merges(communities)

crossing(communities, graph)

code_len(communities)

is_hierarchical(communities)

## S3 method for class 'communities'
as.dendrogram(object, hang = -1, use.modularity = FALSE, ...)

## S3 method for class 'communities'
as.hclust(x, hang = -1, use.modularity = FALSE, ...)

cut_at(communities, no, steps)

show_trace(communities)

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

communities(x)

Arguments

communities, x, object

A communities object, the result of an igraph community detection function.

...

Additional arguments. plot.communities passes these to plot.igraph(). The other functions silently ignore them.

graph

An igraph graph object, corresponding to communities.

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.

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.

y

An igraph graph object, corresponding to the communities in x.

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 do not want to highlight any groups.

edge.color

The colors of the edges. By default the edges within communities are colored green and other edges are red.

membership

Numeric vector, one value for each vertex, the membership vector of the community structure. Might also be NULL if the community structure is given in another way, e.g. by a merge matrix.

algorithm

If not NULL (meaning an unknown algorithm), then a character scalar, the name of the algorithm that produced the community structure.

merges

If not NULL, then the merge matrix of the hierarchical community structure. See merges() below for more information on its format.

modularity

Numeric scalar or vector, the modularity value of the community structure. It can also be NULL, if the modularity of the (best) split is not available.

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 community 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.

communities() is also the name of a function, that returns a list of communities, each identified by their vertices. The vertices will have symbolic names if the add.vertex.names igraph option is set, and the graph itself was named. Otherwise numeric vertex ids are used.

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(), cut_at() 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.

cut_at() 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 stats::dendrogram() for details.

stats::as.hclust() is similar to as.dendrogram(), but converts a hierarchical community structure to a hclust object.

ape::as.phylo() converts a hierarchical community structure to a phylo object, you will need the ape package for this.

show_trace() works (currently) only for communities found by the leading eigenvector method (cluster_leading_eigen()), and returns a character vector that gives the steps performed by the algorithm while finding the communities.

code_len() is defined for the InfoMAP method (cluster_infomap() 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.

cut_at() returns a numeric vector, the membership vector of the vertices.

as.dendrogram() returns a dendrogram object.

show_trace() returns a character vector.

code_len() returns a numeric scalar for communities found with the InfoMAP method and NULL for other methods.

plot() for communities objects returns NULL, invisibly.

Author(s)

Gabor Csardi [e-mail]

See Also

See plot_dendrogram() for plotting community structure dendrograms.

See compare() for comparing two community structures on the same graph.

Community detection as_membership(), cluster_edge_betweenness(), cluster_fast_greedy(), cluster_fluid_communities(), cluster_infomap(), cluster_label_prop(), cluster_leading_eigen(), cluster_leiden(), cluster_louvain(), cluster_optimal(), cluster_spinglass(), cluster_walktrap(), compare(), groups(), make_clusters(), modularity.igraph(), plot_dendrogram(), split_join_distance(), voronoi_cells()

Examples

karate <- make_graph("Zachary")
wc <- cluster_walktrap(karate)
modularity(wc)
membership(wc)
plot(wc, karate)