| cohesive.blocks {igraph} | R Documentation |
Calculates cohesive blocks for objects of class igraph.
cohesive.blocks(graph, labels = TRUE)
blocks(blocks)
blockGraphs(blocks, graph)
cohesion(blocks)
hierarchy(blocks)
parent(blocks)
plotHierarchy(blocks,
layout=layout.reingold.tilford(hierarchy(blocks), root=1), ...)
exportPajek(blocks, graph, file, project.file = TRUE)
maxcohesion(blocks)
## S3 method for class 'cohesiveBlocks'
print(x, ...)
## S3 method for class 'cohesiveBlocks'
summary(object, ...)
## S3 method for class 'cohesiveBlocks'
length(x)
## S3 method for class 'cohesiveBlocks'
plot(x, y, colbar = rainbow(max(cohesion(x))+1),
col = colbar[maxcohesion(x)+1], mark.groups = blocks(x)[-1], ...)
graph |
For For |
labels |
Logical scalar, whether to add the vertex labels to the result object. These labels can be then used when reporting and plotting the cohesive blocks. |
blocks,x,object |
A |
file |
Defines the file (or connection) the Pajek file is written to. If the If the See also details below. |
project.file |
Logical scalar, whether to create a single Pajek project file containing all the data, or to create separated files for each item. See details below. |
y |
The graph whose cohesive blocks are supplied in the
|
colbar |
Color bar for the vertex colors. Its length should be
at least m+1, where m is the maximum cohesion in the
graph. Alternatively, the vertex colors can also be directly
specified via the |
col |
A vector of vertex colors, in any of the usual
formats. (Symbolic color names (e.g. ‘red’, ‘blue’,
etc.) , RGB colors (e.g. ‘#FF9900FF’), integer numbers
referring to the current palette. By default the given
|
mark.groups |
A list of vertex sets to mark on the plot by circling them. By default all cohesive blocks are marked, except the one corresponding to the all vertices. |
layout |
The layout of a plot, it is simply passed on to
|
... |
Additional arguments. |
Cohesive blocking is a method of determining hierarchical subsets of graph vertices based on their structural cohesion (or vertex connectivity). For a given graph G, a subset of its vertices S is said to be maximally k-cohesive if there is no superset of S with vertex connectivity greater than or equal to k. Cohesive blocking is a process through which, given a k-cohesive set of vertices, maximally l-cohesive subsets are recursively identified with l>k. Thus a hiearchy of vertex subsets is found, whith the entire graph G at its root.
The function cohesive.blocks implements cohesive blocking.
It returns a cohesiveBlocks object. cohesiveBlocks
should be handled as an opaque class, i.e. its internal structure
should not be accessed directly, but through the functions listed
here.
The function length can be used on cohesiveBlocks
objects and it gives the number of blocks.
The function blocks returns the actual blocks stored in the
cohesiveBlocks object. They are returned in a list of numeric
vectors, each containing vertex ids.
The function blockGraphs is similar, but returns the blocks as
(induced) subgraphs of the input graph. The various (graph, vertex and
edge) attributes are kept in the subgraph.
The function cohesion returns a numeric vector, the cohesion of
the different blocks. The order of the blocks is the same as for
the blocks and blockGraphs functions.
The block hierarchy can be queried using the hierarchy
function. It returns an igraph graph, its vertex ids are ordered
according the order of the blocks in the blocks and
blockGraphs, cohesion, etc. functions.
parent gives the parent vertex of each block, in the block
hierarchy, for the root vertex it gives 0.
plotHierarchy plots the hierarchy tree of the cohesive blocks
on the active graphics device, by calling igraph.plot.
The exportPajek function can be used to export the graph and
its cohesive blocks in Pajek format. It can either export a single
Pajek project file with all the information, or a set of files,
depending on its project.file argument. If project.file
is TRUE, then the following information is written to the file
(or connection) given in the file argument: (1) the input
graph, together with its attributes, see write.graph for
details; (2) the hierarchy graph; and (3) one binary partition for
each cohesive block. If project.file is FALSE, then the
file argument must be a character scalar and it is used as the
base name for the generated files. If file is
‘basename’, then the following files are created: (1)
‘basename.net’ for the original graph; (2)
‘basename_hierarchy.net’ for the hierarchy graph; (3)
‘basename_block_x.net’ for each cohesive block, where
‘x’ is the number of the block, starting with one.
maxcohesion returns the maximal cohesion of each vertex,
i.e. the cohesion of the most cohesive block of the vertex.
The generic function summary works on cohesiveBlocks
objects and it prints a one line summary to the terminal.
The generic function print is also defined on
cohesiveBlocks objects and it is invoked automatically if the
name of the cohesiveBlocks object is typed in. It produces
an output like this:
Cohesive block structure:
B-1 c 1, n 23
'- B-2 c 2, n 14 oooooooo.. .o......oo ooo
'- B-4 c 5, n 7 ooooooo... .......... ...
'- B-3 c 2, n 10 ......o.oo o.oooooo.. ...
'- B-5 c 3, n 4 ......o.oo o......... ...
The left part shows the block structure, in this case for five
blocks. The first block always corresponds to the whole graph, even if
its cohesion is zero. Then cohesion of the block and the number of
vertices in the block are shown. The last part is only printed if the
display is wide enough and shows the vertices in the blocks,
ordered by vertex ids. ‘o’ means that the vertex is included,
a dot means that it is not, and the vertices are shown in groups of
ten.
The generic function plot plots the graph, showing one or more
cohesive blocks in it.
cohesive.blocks returns a cohesiveBlocks
object.
blocks returns a list of numeric vectors, containing vertex
ids.
blockGraphs returns a list of igraph graphs, corresponding to
the cohesive blocks.
cohesion returns a numeric vector, the cohesion of each block.
hierarchy returns an igraph graph, the representation of the
cohesive block hierarchy.
parent returns a numeric vector giving the parent block of each
cohesive block, in the block hierarchy. The block at the root of the
hierarchy has no parent and 0 is returned for it.
plotHierarchy, plot and exportPajek return
NULL, invisibly.
maxcohesion returns a numeric vector with one entry for each
vertex, giving the cohesion of its most cohesive block.
print and summary return the cohesiveBlocks
object itself, invisibly.
length returns a numeric scalar, the number of blocks.
Gabor Csardi csardi.gabor@gmail.com for the current implementation, Peter McMahan (http://home.uchicago.edu/~mcmahan/) wrote the first version in R.
J. Moody and D. R. White. Structural cohesion and embeddedness: A hierarchical concept of social groups. American Sociological Review, 68(1):103–127, Feb 2003.
## The graph from the Moody-White paper
mw <- graph.formula(1-2:3:4:5:6, 2-3:4:5:7, 3-4:6:7, 4-5:6:7,
5-6:7:21, 6-7, 7-8:11:14:19, 8-9:11:14, 9-10,
10-12:13, 11-12:14, 12-16, 13-16, 14-15, 15-16,
17-18:19:20, 18-20:21, 19-20:22:23, 20-21,
21-22:23, 22-23)
mwBlocks <- cohesive.blocks(mw)
# Inspect block membership and cohesion
mwBlocks
blocks(mwBlocks)
cohesion(mwBlocks)
# Save results in a Pajek file
## Not run:
exportPajek(mwBlocks, mw, file="/tmp/mwBlocks.paj")
## End(Not run)
# Plot the results
if (interactive()) {
plot(mwBlocks, mw)
}
## The science camp network
camp <- graph.formula(Harry:Steve:Don:Bert - Harry:Steve:Don:Bert,
Pam:Brazey:Carol:Pat - Pam:Brazey:Carol:Pat,
Holly - Carol:Pat:Pam:Jennie:Bill,
Bill - Pauline:Michael:Lee:Holly,
Pauline - Bill:Jennie:Ann,
Jennie - Holly:Michael:Lee:Ann:Pauline,
Michael - Bill:Jennie:Ann:Lee:John,
Ann - Michael:Jennie:Pauline,
Lee - Michael:Bill:Jennie,
Gery - Pat:Steve:Russ:John,
Russ - Steve:Bert:Gery:John,
John - Gery:Russ:Michael)
campBlocks <- cohesive.blocks(camp)
campBlocks
if (interactive()) {
plot(campBlocks, camp, vertex.label=V(camp)$name, margin=-0.2,
vertex.shape="rectangle", vertex.size=24, vertex.size2=8,
mark.border=1, colbar=c(NA, NA,"cyan","orange") )
}