# cohesive.blocks

##### Calculate Cohesive Blocks

Calculates cohesive blocks for objects of class `igraph`

.

- Keywords
- graphs

##### Usage

```
cohesive.blocks(graph, db=NULL,
useDB=(vcount(graph)>400 && require(RSQLite)),
cutsetHeuristic=TRUE,
verbose=igraph.par("verbose"))
is.bgraph(graph)
```

##### Arguments

- graph
- A graph object of class
`igraph`

. - db
- An optional
`RSQLite`

connection to an existing SQLite database (see details). Ignored if`NULL`

. - useDB
- Logical. Whether to use an external SQLite database
instead of internal R datastructures (see details). By default an
SQLite database is used if the graph has more than 400 vertices
and the
`RSQLite`

package is installed. - cutsetHeuristic
- Logical scalar. TODO
- verbose
- Level of console output. Supply
`TRUE`

here to follow the progress of the computation.

##### Details

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.

For certain larger graphs this algorithm can be quite memory-intensive
due to the number of vertex subsets that are examined. In these cases it
is worthwhile to use a database to keep track of this data, specified by
the `useDB`

argument. If `useDB`

is `TRUE`

, then either a
temporary SQLite database is created, or the `RSQLite`

connection
specified in `db`

is used. In either case the package
`RSQLite`

will be required.

`structurally.cohesive.blocks`

is an alias to
`cohesive.blocks`

.

`is.bgraph`

decides whether its argument is a `bgraph`

object.

##### Value

`cohesive.blocks`

returns a graph of class`c(bgraph,igraph)`

, with four (new) graph attributes:blocks A list with one element for each cohesive block found. The elements are numeric vectors listing the indices of the nodes within that block. block.cohesion A numeric vector with length equal to the number of cohesive blocks found, listing the cohesion of those blocks. tree The hierarchical tree of the cohesive blocks. Each node of this graph represents a cohesive block, and directed edges represent inclusion as proper subset. data A list containing supplementary data from the calculation. `is.bgraph`

returns a logical scalar.

##### concept

Structurally cohesive blocks

##### References

A. Kanevsky. On the number of minimum size separating vertex sets
in a graph and how to find all of them
*Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms*
San Francisco, California, United States. 411--421, 1990.
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.

##### See Also

`graph.cohesion`

, `plot.bgraph`

for
plotting graphs together with their block hierarchy,
`write.pajek.bgraph`

for a writing graphs and cohesive
blocks information to Pajek files. See `attributes`

for
handling graph attributes.

##### Examples

```
## Create a graph with an interesting structure:
g <- graph.disjoint.union(graph.full(4), graph.empty(2,directed=FALSE))
g <- add.edges(g,c(3,4,4,5,4,2))
g <- graph.disjoint.union(g,g,g)
g <- add.edges(g,c(0,6,1,7,0,12,4,0,4,1))
## Find cohesive blocks:
gBlocks <- cohesive.blocks(g)
## Examine block membership and cohesion:
gBlocks$blocks
gBlocks$block.cohesion
## Plot the resulting graph with its block hierarchy:
plot(gBlocks, vertex.size=7, layout=layout.kamada.kawai)
## Save the results as Pajek ".net" and ".clu" files:
write.pajek.bgraph(gBlocks,file="gBlocks")
## An example that works better with the "kanevsky" cutset algorithm
g <- read.graph(file="http://intersci.ss.uci.edu/wiki/Vlado/SanJuanSur.net", format="pajek")
gBlocks <- cohesive.blocks(g, cutsetAlgorithm="kanevsky")
```

*Documentation reproduced from package igraph, version 0.5.5-3, License: GPL (>= 2)*