Calculate Cohesive Blocks
Calculates cohesive blocks for objects of class
cohesive_blocks(graph, labels = TRUE)
## S3 method for class 'cohesiveBlocks': length(x)
## S3 method for class 'cohesiveBlocks': cohesion(x, ...)
## S3 method for class 'cohesiveBlocks': print(x, ...)
## S3 method for class 'cohesiveBlocks': summary(object, ...)
## S3 method for class 'cohesiveBlocks': plot(x, y, colbar = rainbow(max(cohesion(x)) + 1), col = colbar[max_cohesion(x) + 1], mark.groups = blocks(x)[-1], ...)
plot_hierarchy(blocks, layout = layout_as_tree(hierarchy(blocks), root = 1), ...)
export_pajek(blocks, graph, file, project.file = TRUE)
cohesive_blocksa graph object of class
igraph. It must be undirected and simple. (See
- 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.
cohesiveBlocksobject, created with the
- The graph whose cohesive blocks are supplied in the
- 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
- 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 <
- 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.
- The layout of a plot, it is simply passed on to
plot.igraph, see the possible formats there. By default the Reingold-Tilford layout generator is used.
- Defines the file (or connection) the Pajek file is written to.
TRUE, then it can be a filename (with extension), a file object, or in general any king of connection object. The file/connection wil
- 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.
- Additional arguments.
plotpass them to
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 $S\subset V(G)$ 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.
cohesive_blocks implements cohesive blocking. It
cohesiveBlocks should be
handled as an opaque class, i.e. its internal structure should not be
accessed directly, but through the functions listed here.
length can be used on
cohesiveBlocks objects and
it gives the number of blocks.
blocks returns the actual blocks stored in the
cohesiveBlocks object. They are returned in a list of numeric
vectors, each containing vertex ids.
graphs_from_cohesive_blocks 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.
cohesion returns a numeric vector, the cohesion of the
different blocks. The order of the blocks is the same as for the
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
parent gives the parent vertex of each block, in the block hierarchy,
for the root vertex it gives 0.
plot_hierarchy plots the hierarchy tree of the cohesive blocks on the
active graphics device, by calling
export_pajek 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
the following information is written to the file (or connection) given in
file argument: (1) the input graph, together with its attributes,
write_graph for details; (2) the hierarchy graph; and (3)
one binary partition for each cohesive block. If
FALSE, then the
file argument must be a character scalar and
it is used as the base name for the generated files. If
max_cohesion 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
and it prints a one line summary to the terminal.
The generic function
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.
The generic function
plot plots the graph, showing one or more
cohesive blocks in it.
blocksreturns a list of numeric vectors, containing vertex ids.
graphs_from_cohesive_blocksreturns a list of igraph graphs, corresponding to the cohesive blocks.
cohesionreturns a numeric vector, the cohesion of each block.
hierarchyreturns an igraph graph, the representation of the cohesive block hierarchy.
parentreturns 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
0is returned for it.
max_cohesionreturns a numeric vector with one entry for each vertex, giving the cohesion of its most cohesive block.
cohesiveBlocksobject itself, invisibly.
lengthreturns a numeric scalar, the number of blocks.
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_from_literal(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 export_pajek(mwBlocks, mw, file="/tmp/mwBlocks.paj") # Plot the results plot(mwBlocks, mw) ## The science camp network camp <- graph_from_literal(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 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") )