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#' Calculate Cohesive Blocks
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `exportPajek()` was renamed to `export_pajek()` to create a more
#' consistent API.
#' @inheritParams export_pajek
#' @keywords internal
#' @export
exportPajek <- function(blocks, graph, file, project.file = TRUE) { # nocov start
lifecycle::deprecate_soft("2.0.0", "exportPajek()", "export_pajek()")
export_pajek(blocks = blocks, graph = graph, file = file, project.file = project.file)
} # nocov end
#' Calculate Cohesive Blocks
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `plotHierarchy()` was renamed to `plot_hierarchy()` to create a more
#' consistent API.
#' @inheritParams plot_hierarchy
#' @keywords internal
#' @export
plotHierarchy <- function(blocks, layout = layout_as_tree(hierarchy(blocks), root = 1), ...) { # nocov start
lifecycle::deprecate_soft("2.0.0", "plotHierarchy()", "plot_hierarchy()")
plot_hierarchy(blocks = blocks, layout = layout, ...)
} # nocov end
#' Calculate Cohesive Blocks
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `maxcohesion()` was renamed to `max_cohesion()` to create a more
#' consistent API.
#' @inheritParams max_cohesion
#' @keywords internal
#' @export
maxcohesion <- function(blocks) { # nocov start
lifecycle::deprecate_soft("2.0.0", "maxcohesion()", "max_cohesion()")
max_cohesion(blocks = blocks)
} # nocov end
#' Vertex connectivity
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `graph.cohesion()` was renamed to `cohesion()` to create a more
#' consistent API.
#' @param x x
#' @param ... passed to `cohesion()`
#' @keywords internal
#' @export
graph.cohesion <- function(x, ...) { # nocov start
lifecycle::deprecate_soft("2.0.0", "graph.cohesion()", "cohesion()")
cohesion(x = x, ...)
} # nocov end
#' Calculate Cohesive Blocks
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `cohesive.blocks()` was renamed to `cohesive_blocks()` to create a more
#' consistent API.
#' @inheritParams cohesive_blocks
#' @keywords internal
#' @export
cohesive.blocks <- function(graph, labels = TRUE) { # nocov start
lifecycle::deprecate_soft("2.0.0", "cohesive.blocks()", "cohesive_blocks()")
cohesive_blocks(graph = graph, labels = labels)
} # nocov end
#' Calculate Cohesive Blocks
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `blockGraphs()` was renamed to `graphs_from_cohesive_blocks()` to create a more
#' consistent API.
#' @inheritParams graphs_from_cohesive_blocks
#' @keywords internal
#' @export
blockGraphs <- function(blocks, graph) { # nocov start
lifecycle::deprecate_soft("2.0.0", "blockGraphs()", "graphs_from_cohesive_blocks()")
graphs_from_cohesive_blocks(blocks = blocks, graph = graph)
} # nocov end
# IGraph R package
# Copyright (C) 2010-2012 Gabor Csardi <csardi.gabor@gmail.com>
# 334 Harvard street, Cambridge, MA 02139 USA
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
# 02110-1301 USA
#
###################################################################
#' Calculate Cohesive Blocks
#'
#' Calculates cohesive blocks for objects of class `igraph`.
#'
#' Cohesive blocking is a method of determining hierarchical subsets of graph
#' vertices based on their structural cohesion (or vertex connectivity). For a
#' given graph \eqn{G}, a subset of its vertices \eqn{S\subset V(G)}{S} is said
#' to be maximally \eqn{k}-cohesive if there is no superset of \eqn{S} with
#' vertex connectivity greater than or equal to \eqn{k}. Cohesive blocking is a
#' process through which, given a \eqn{k}-cohesive set of vertices, maximally
#' \eqn{l}-cohesive subsets are recursively identified with \eqn{l>k}. Thus a
#' hierarchy of vertex subsets is found, with the entire graph \eqn{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 `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.
#'
#' 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 `graphs_from_cohesive_blocks()` 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 `graphs_from_cohesive_blocks()`, `cohesion()`,
#' etc. functions.
#'
#' `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 `igraph.plot`.
#'
#' The `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 `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
#' \sQuote{basename}, then the following files are created: (1)
#' \sQuote{basename.net} for the original graph; (2)
#' \sQuote{basename_hierarchy.net} for the hierarchy graph; (3)
#' \sQuote{basename_block_x.net} for each cohesive block, where \sQuote{x} is
#' the number of the block, starting with one.
#'
#' `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 `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:
#' \preformatted{ 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.
#' \sQuote{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.
#'
#' @aliases cohesiveBlocks blocks
#' @aliases hierarchy parent export_pajek plot.cohesiveBlocks
#' summary.cohesiveBlocks length.cohesiveBlocks print.cohesiveBlocks
#' @param graph For `cohesive_blocks()` a graph object of class
#' `igraph`. It must be undirected and simple. (See
#' [is_simple()].)
#'
#' For `graphs_from_cohesive_blocks()` and `export_pajek()` the same graph must be
#' supplied whose cohesive block structure is given in the `blocks()`
#' argument.
#' @param 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.
#' @param blocks,x,object A `cohesiveBlocks` object, created with the
#' `cohesive_blocks()` function.
#' @param file Defines the file (or connection) the Pajek file is written to.
#'
#' If the `project.file` argument is `TRUE`, then it can be a
#' filename (with extension), a file object, or in general any king of
#' connection object. The file/connection will be opened if it wasn't already.
#'
#' If the `project.file` argument is `FALSE`, then several files are
#' created and `file` must be a character scalar containing the base name
#' of the files, without extension. (But it can contain the path to the files.)
#'
#' See also details below.
#' @param 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.
#' @param y The graph whose cohesive blocks are supplied in the `x`
#' argument.
#' @param colbar Color bar for the vertex colors. Its length should be at least
#' \eqn{m+1}, where \eqn{m} is the maximum cohesion in the graph.
#' Alternatively, the vertex colors can also be directly specified via the
#' `col` argument.
#' @param col A vector of vertex colors, in any of the usual formats. (Symbolic
#' color names (e.g. \sQuote{red}, \sQuote{blue}, etc.) , RGB colors (e.g.
#' \sQuote{#FF9900FF}), integer numbers referring to the current palette. By
#' default the given `colbar` is used and vertices with the same maximal
#' cohesion will have the same color.
#' @param 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.
#' @param layout 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.
#' @param \dots Additional arguments. `plot_hierarchy()` and [plot()] pass
#' them to `plot.igraph()`. [print()] and [summary()] ignore them.
#' @return `cohesive_blocks()` returns a `cohesiveBlocks` object.
#'
#' `blocks()` returns a list of numeric vectors, containing vertex ids.
#'
#' `graphs_from_cohesive_blocks()` 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.
#'
#' `plot_hierarchy()`, [plot()] and `export_pajek()` return `NULL`,
#' invisibly.
#'
#' `max_cohesion()` 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.
#' @author Gabor Csardi \email{csardi.gabor@gmail.com} for the current
#' implementation, Peter McMahan (<https://socialsciences.uchicago.edu/news/alumni-profile-peter-mcmahan-phd17-sociology>)
#' wrote the first version in R.
#' @seealso [cohesion()]
#' @references 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, \doi{10.2307/3088904}.
#' @family cohesive.blocks
#' @export
#' @keywords graphs
#' @examples
#'
#' ## 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
#' file <- tempfile(fileext = ".paj")
#' export_pajek(mwBlocks, mw, file = file)
#' if (!interactive()) {
#' unlink(file)
#' }
#'
#' # 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)$name, margin = -0.2,
#' vertex.shape = "rectangle", vertex.size = 24, vertex.size2 = 8,
#' mark.border = 1, colbar = c(NA, NA, "cyan", "orange")
#' )
#'
cohesive_blocks <- function(graph, labels = TRUE) {
# Argument checks
ensure_igraph(graph)
on.exit(.Call(R_igraph_finalizer))
# Function call
res <- .Call(R_igraph_cohesive_blocks, graph)
class(res) <- "cohesiveBlocks"
if (labels && "name" %in% vertex_attr_names(graph)) {
res$labels <- V(graph)$name
}
if (igraph_opt("return.vs.es")) {
res$blocks <- lapply(res$blocks, unsafe_create_vs, graph = graph, verts = V(graph))
}
res$vcount <- vcount(graph)
res
}
#' @rdname cohesive_blocks
#' @method length cohesiveBlocks
#' @family cohesive.blocks
#' @export
length.cohesiveBlocks <- function(x) {
length(x$blocks)
}
#' @rdname cohesive_blocks
#' @export
blocks <- function(blocks) {
blocks$blocks
}
#' @rdname cohesive_blocks
#' @export
graphs_from_cohesive_blocks <- function(blocks, graph) {
lapply(blocks(blocks), induced_subgraph, graph = graph)
}
#' @family cohesive.blocks
#' @export
cohesion <- function(x, ...) {
UseMethod("cohesion")
}
#' @rdname cohesive_blocks
#' @method cohesion cohesiveBlocks
#' @export
cohesion.cohesiveBlocks <- function(x, ...) {
x$cohesion
}
#' @rdname cohesive_blocks
#' @export
hierarchy <- function(blocks) {
blocks$blockTree
}
#' @rdname cohesive_blocks
#' @export
parent <- function(blocks) {
blocks$parent
}
#' @rdname cohesive_blocks
#' @method print cohesiveBlocks
#' @export
print.cohesiveBlocks <- function(x, ...) {
cat("Cohesive block structure:\n")
myb <- blocks(x)
ch <- cohesion(x)
pp <- parent(x)
si <- sapply(myb, length)
cs <- 3 + 2 + nchar(length(x)) +
max(distances(hierarchy(x), mode = "out", v = 1)) * 3
.plot <- function(b, ind = "") {
if (b != 1) {
he <- format(paste(sep = "", ind, "'- B-", b), width = cs)
ind <- paste(" ", ind)
} else {
he <- format(paste(sep = "", "B-", b), width = cs)
}
cat(
sep = "", he,
"c ", format(ch[b], width = nchar(max(ch)), justify = "right"),
", n ", format(si[b], width = nchar(x$vcount), justify = "right")
)
if (x$vcount <= options("width")$width - 40 && b != 1) {
o <- rep(".", x$vcount)
o[myb[[b]]] <- "o"
oo <- character()
for (i in 1:floor(x$vcount / 10)) {
oo <- c(oo, o[((i - 1) * 10 + 1):(i * 10)], " ")
}
if (x$vcount %% 10) {
oo <- c(oo, o[(i * 10 + 1):length(o)])
}
cat(" ", paste(oo, collapse = ""), "\n")
} else {
cat("\n")
}
wc <- which(pp == b)
sapply(wc, .plot, ind = ind)
}
if (length(x) > 0) .plot(1) else cat("No cohesive blocks found.")
invisible(x)
}
#' @rdname cohesive_blocks
#' @method summary cohesiveBlocks
#' @family cohesive.blocks
#' @export
summary.cohesiveBlocks <- function(object, ...) {
cat(
"Structurally cohesive block structure, with",
length(blocks(object)), "blocks.\n"
)
invisible(object)
}
#' @rdname cohesive_blocks
#' @method plot cohesiveBlocks
#' @export
#' @importFrom grDevices rainbow
#' @importFrom graphics plot
plot.cohesiveBlocks <- function(x, y,
colbar = rainbow(max(cohesion(x)) + 1),
col = colbar[max_cohesion(x) + 1],
mark.groups = blocks(x)[-1],
...) {
plot(y,
mark.groups = mark.groups,
vertex.color = col, ...
)
}
#' @rdname cohesive_blocks
#' @export
#' @importFrom graphics plot
plot_hierarchy <- function(blocks,
layout = layout_as_tree(hierarchy(blocks),
root = 1
), ...) {
plot(hierarchy(blocks), layout = layout, ...)
}
exportPajek.cohesiveblocks.pf <- function(blocks, graph, file) {
closeit <- FALSE
if (is.character(file)) {
file <- file(file, open = "w+b")
closeit <- TRUE
}
if (!isOpen(file)) {
file <- open(file)
closeit <- TRUE
}
## The original graph
cat(file = file, sep = "", "*Network cohesive_blocks_input.net\r\n")
write_graph(graph, file = file, format = "pajek")
## The hierarchy graph
cat(file = file, sep = "", "\r\n*Network hierarchy.net\r\n")
write_graph(hierarchy(blocks), file = file, format = "pajek")
## The blocks
myb <- blocks(blocks)
for (b in seq_along(myb)) {
thisb <- rep(0, vcount(graph))
thisb[myb[[b]]] <- 1
cat(
file = file, sep = "", "\r\n*Partition block_", b, ".clu\r\n",
"*Vertices ", vcount(graph), "\r\n "
)
cat(thisb, sep = "\r\n ", file = file)
}
if (closeit) {
close(file)
}
invisible(NULL)
}
exportPajek.cohesiveblocks.nopf <- function(blocks, graph, file) {
## The original graph
write_graph(graph, file = paste(sep = "", file, ".net"), format = "pajek")
## The hierarchy graph
write_graph(hierarchy(blocks),
file = paste(sep = "", file, "_hierarchy.net"),
format = "pajek"
)
## The blocks
myb <- blocks(blocks)
for (b in seq_along(myb)) {
thisb <- rep(0, vcount(graph))
thisb[myb[[b]]] <- 1
cat(
file = paste(sep = "", file, "_block_", b, ".clu"), sep = "\r\n",
paste("*Vertices", vcount(graph)), thisb
)
}
invisible(NULL)
}
#' @rdname cohesive_blocks
#' @export
export_pajek <- function(blocks, graph, file,
project.file = TRUE) {
if (!project.file && !is.character(file)) {
stop(paste(
"`file' must be a filename (without extension) when writing",
"to separate files"
))
}
if (project.file) {
return(exportPajek.cohesiveblocks.pf(blocks, graph, file))
} else {
return(exportPajek.cohesiveblocks.nopf(blocks, graph, file))
}
}
#' @rdname cohesive_blocks
#' @export
max_cohesion <- function(blocks) {
res <- numeric(blocks$vcount)
myb <- blocks(blocks)
coh <- cohesion(blocks)
oo <- order(coh)
myb <- myb[oo]
coh <- coh[oo]
for (b in seq_along(myb)) {
res[myb[[b]]] <- coh[b]
}
res
}
#########################################################
## Various designs to print the cohesive blocks
## Cohesive block structure:
## B-1 c. 1, n. 34
## '- B-2 c. 2, n. 28 1,2,3,4,8,9,10,13,14,15,16,18,19,20,21,22,
## | 23,24,25,26,27,28,29,30,31,32,33,34
## '- B-4 c. 4, n. 5 1,2,3,4,8
## '- B-5 c. 3, n. 7 1,2,3,9,31,33,34
## '- B-7 c. 4, n. 5 1,2,3,4,14
## '- B-8 c. 3, n. 10 3,24,25,26,28,29,30,32,33,34
## '- B-3 c. 2, n. 6 1,5,6,7,11,17
## '- B-6 c. 3, n. 5 1,5,6,7,11
## Cohesive block structure:
## B-1 c. 1, n. 23
## '- B-2 c. 2, n. 14 1,2,3,4,5,6,7,8,12,19,20,21,22,23
## '- B-4 c. 5, n. 7 1,2,3,4,5,6,7
## '- B-3 c. 2, n. 10 7,9,10,11,13,14,15,16,17,18
## '- B-5 c. 3, n. 4 7,9,10,11
## #########################################################
## Cohesive block structure:
## B-1 c 1, n 34
## '- B-2 c 2, n 28 oooo...ooo ..oooo.ooo oooooooooo oooo
## '- B-4 c 4, n 5 oooo...o.. .......... .......... ....
## '- B-5 c 3, n 7 ooo.....o. .......... .......... o.oo
## '- B-7 c 4, n 5 oooo...... ...o...... .......... ....
## '- B-8 c 3, n 10 ..o....... .......... ...ooo.ooo .ooo
## '- B-3 c 2, n 6 o...ooo... o.....o... .......... ....
## '- B-6 c 3, n 5 o...ooo... o......... .......... ....
## Cohesive block structure:
## B-1 c 1, n 23 oooooooooo oooooooooo ooo
## '- 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......... ...
## #########################################################
## Cohesive block structure:
## B-1 c. 1, n. 34
## '- B-2 c. 2, n. 28 1, 2, 3, 4, 8, 9,10,13,14,15,16,18,19,20,21,
## | 22,23,24,25,26,27,28,29,30,31,32,33,34
## '- B-4 c. 4, n. 5 1, 2, 3, 4, 8
## '- B-5 c. 3, n. 7 1, 2, 3, 9,31,33,34
## '- B-7 c. 4, n. 5 1, 2, 3, 4,14
## '- B-8 c. 3, n. 10 3,24,25,26,28,29,30,32,33,34
## '- B-3 c. 2, n. 6 1, 5, 6, 7,11,17
## '- B-6 c. 3, n. 5 1, 5, 6, 7,11
## Cohesive block structure:
## B-1 c. 1, n. 23
## '- B-2 c. 2, n. 14 1, 2, 3, 4, 5, 6, 7, 8,12,19,20,21,22,23
## '- B-4 c. 5, n. 7 1, 2, 3, 4, 5, 6, 7
## '- B-3 c. 2, n. 10 7, 9,10,11,13,14,15,16,17,18
## '- B-5 c. 3, n. 4 7, 9,10,11
## #########################################################
## Cohesive block structure:
## B-1 c. 1, n. 34
## '- B-2 c. 2, n. 28 1-4, 8-10, 13-16, 18-34
## '- B-4 c. 4, n. 5 1-4, 8
## '- B-5 c. 3, n. 7 1-3, 9, 31, 33-34
## '- B-7 c. 4, n. 5 1-4, 14
## '- B-8 c. 3, n. 10 3, 24-26, 28-30, 32-34
## '- B-3 c. 2, n. 6 1, 5-7, 11, 17
## '- B-6 c. 3, n. 5 1, 5-7, 11
## Cohesive block structure:
## B-1 c. 1, n. 23
## '- B-2 c. 2, n. 14 1-8, 12, 19-23
## '- B-4 c. 5, n. 7 1-7
## '- B-3 c. 2, n. 10 7, 9-11, 13-18
## '- B-5 c. 3, n. 4 7, 9-11
## ##########################################################
## Cohesive block structure:
## B-1 c. 1, n. 34
## |- B-2 c. 2, n. 28 [ 1] oooo...ooo ..oooo.ooo
## | | [21] oooooooooo oooo
## | |- B-4 c. 4, n. 5 [ 1] oooo...o.. ..........
## | | [21] .......... ....
## | |- B-5 c. 3, n. 7 [ 1] ooo.....o. ..........
## | | [21] .......... o.oo
## | |- B-7 c. 4, n. 5 [ 1] oooo...... ...o......
## | | [21] .......... ....
## | |- B-8 c. 3, n. 10 [ 1] ..o....... ..........
## | [21] ...ooo.ooo .ooo
## '- B-3 c. 2, n. 6 [ 1] o...ooo... o.....o...
## | [21] .......... ....
## '- B-6 c. 3, n. 5 [ 1] o...ooo... o.........
## [21] .......... ....
## Cohesive block structure:
## B-1 c. 1, n. 23 [ 1] oooooooooo oooooooooo
## | [21] ooo
## |- B-2 c. 2, n. 14 [ 1] oooooooo.. .o......oo
## | | [21] ooo
## | '- B-4 c. 5, n. 7 [ 1] ooooooo... ..........
## | [21] ...
## '- B-3 c. 2, n. 10 [ 1] ......o.oo o.oooooo..
## | [21] ...
## '- B-5 c. 3, n. 4 [ 1] ......o.oo o.........
## [21] ...
|