Type:	Package
Title:	CONCOR and Supplemental Functions
Version:	0.2.1
Description:	Contains the CONCOR (CONvergence of iterated CORrelations) algorithm and a series of supplemental functions for easy running, plotting, and blockmodeling. The CONCOR algorithm is used on social network data to identify network positions based off a definition of structural equivalence; see Breiger, Boorman, and Arabie (1975) <doi:10.1016/0022-2496(75)90028-0> and Wasserman and Faust's book Social Network Analysis: Methods and Applications (1994). This version allows multiple relationships for the same set of nodes and uses both incoming and outgoing ties to find positions.
Imports:	igraph, sna, stats, graphics
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
LazyData:	true
URL:	https://github.com/ATraxLab/concorR
BugReports:	https://github.com/ATraxLab/concorR/issues
RoxygenNote:	7.1.0
NeedsCompilation:	no
Packaged:	2020-11-25 20:14:37 UTC; w039alt
Author:	Tyme Suda [aut], Adrienne Traxler [cre], Carter Butts [ctb] (Author of sna::plot.blockmodel(), adapted for plot_blk())
Maintainer:	Adrienne Traxler <adrienne.traxler@wright.edu>
Repository:	CRAN
Date/Publication:	2020-11-25 20:30:07 UTC

Find CONCOR partition for a graph

Description

Use the CONCOR (CONvergence of iterated CORrelations) algorithm to identify roles within social network data.

Usage

concor(m_list, nsplit = 1, self_ties = FALSE, cutoff = .9999999, max_iter = 50)

Arguments

Details

This version works for multiple relationships, assuming they all are for the same data (same size of input matrices), and can be used with isolates present. It requires further testing on weighted networks (but appears to successfully split such networks). It will attempt to split the network nsplit times, causing there to be 2^nsplit partitions, plus one for isolated nodes (if they exist), unless a structurally equivalent node group or singular node group is present. If the algorithm attempts to split such a node group the function will ignore that group and continue to split all other blocks until specified. If a higher number of splits, nsplit, are requested than are possible to apply to the specified data (due to structurally equivalent node groups being present or all blocks being singular nodes) the code will warn the user that split nsplit was the same as split i, the final possible split, and stop.

Value

A data frame with two columns: block is the block or role identified by CONCOR, and vertex is the node names.

References

R. L. Breiger, S. A. Boorman, P. Arabie, An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling. J. of Mathematical Psychology. 12, 328 (1975). doi: 10.1016/0022-2496(75)90028-0

S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, 1994).

Examples

a <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(a) <- c("a", "b", "c", "d")
colnames(a) <- c("a", "b", "c", "d")

concor(list(a))

Find +1/-1 convergence points of an input matrix

Description

A subfunction of concor.

Runs the Pearson correlation on the matrix stack repeatedly until a square matrix consisting of only +1 and -1 is formed.

Usage

concor1(m_stack, cutoff = .9999999, max_iter = 50)

Arguments

Details

For network data with R relations, the input matrix "stack" is a (2 x N x R) x N matrix, consisting of each relation's adjacency matrix, then the transpose of that matrix, appended to each other vertically. The correlation is run until either all matrix entries have absolute values greater than cutoff or the maximum number of iterations max_iter is reached. On its own, this function does not execute the whole CONCOR method, but is listed separately from concor to demonstrate the core step.

Value

A square matrix, with number of rows/columns equal to the number of columns of m_stack, where the values are either +1 or -1. The input matrix can later be split into two "positions" based off the locations of the positive/negative values.

See Also

concor

Examples

a <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
b <- rbind(a, t(a))

concor1(b)

The concorR Package

Description

concorR implements the CONCOR (CONvergence of iterated CORrelations) algorithm as introduced by Breiger, Boorman, and Arabie (1975) and detailed by Wasserman and Faust (1994). This package includes the concor algorithm itself, and some useful functions for plotting and interpreting the outputs. The plotting methods included are: plotting the overall network with the concor partitions as colors (using the igraph package), plotting a blockmodel using the concor partitions (using the sna package), and plotting reduced network graphs showing the connections between concor partitions (again using igraph).

Author(s)

Tyme Suda suda.4@wright.edu

Adrienne Traxler adrienne.traxler@wright.edu

This work was supported by National Science Foundation awards DUE-1712341 and DUE-1711017.

References

R. L. Breiger, S. A. Boorman, P. Arabie, An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling. J. of Mathematical Psychology. 12, 328 (1975). doi: 10.1016/0022-2496(75)90028-0

S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, 1994).

Find CONCOR partition and add to a list of igraph objects

Description

Takes a list of igraph objects, runs concor until the desired number of splits, and adds the final split to each object as a vertex attribute.

Usage

concor_igraph_apply(igraph_list, nsplit = 1)

Arguments

Details

This function is a wrapper for a common task: Running concor on one or more igraph objects and adding the resulting partition to each object as a vertex attribute. If multiple igraph objects are included in the input list, they should be multiple relations for the same nodes.

If all of the input graphs are weighted, edge weights will be used by concor.

Value

Returns a list of igraph objects, each with a vertex attribute csplitn (where n is nsplit) that contains the block assignment obtained from concor.

See Also

concor, concor_make_igraph

Examples

a <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(a) <- c("a", "b", "c", "d")
colnames(a) <- c("a", "b", "c", "d")
a.igraph <- igraph::graph_from_adjacency_matrix(a)
concor_igraph_apply(list(a.igraph))

b <- matrix(c(0, 0, 0, 4, 1, 0, 3, 0, 2, 1, 0, 1, 1, 0, 2, 0), ncol = 4)
rownames(b) <- c("a", "b", "c", "d")
colnames(b) <- c("a", "b", "c", "d")
b.igraph <- igraph::graph_from_adjacency_matrix(b, weighted = "weight")
concor_igraph_apply(list(b.igraph))

concor_igraph_apply(list(a.igraph, b.igraph))

Find CONCOR partition and create a list of igraph objects

Description

Run concor on a list of adjacency matrices and create a list of igraph objects with a specific CONCOR split added as a vertex attribute.

Usage

concor_make_igraph(adj_list, nsplit = 1)

Arguments

Details

This function is a wrapper for a common task: Running concor on one or more adjacency matrices, then saving the networks as igraph objects with the CONCOR partition as a vertex attribute. If multiple adjacency matrices are included in the input list, they should be multiple relations for the same nodes.

If any of the input matrices have entries other than 0 and 1, all are treated as weighted (a weight edge attribute is added to each output graph).

Value

Returns a list of igraph objects with a vertex attribute csplitn, where n is nsplit that contains the block assignment obtained from concor.

See Also

concor, concor_igraph_apply

Examples

a <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(a) <- c("a", "b", "c", "d")
colnames(a) <- c("a", "b", "c", "d")
concor_make_igraph(list(a))

b <- matrix(c(0, 0, 0, 4, 1, 0, 3, 0, 2, 1, 0, 1, 1, 0, 2, 0), ncol = 4)
rownames(b) <- c("a", "b", "c", "d")
colnames(b) <- c("a", "b", "c", "d")
concor_make_igraph(list(b))

concor_make_igraph(list(a, b))

Krackhardt High-Tech Managers data

Description

A network of connections between 21 managers at a manufacturing company taken by David Krackhardt in 1987. The three networks available are advice, friendship, and report structure.

Usage

krack_advice

krack_friend

krack_report

Format

A directed and unweighted igraph object.

Vertex attributes:

• Name: Vertex names (character; "v1", "v2", ..., "v21").

• x,y: A set of plotting coordinates, used if no other layout is supplied (numeric).

• Age: The age of each manager (integer).

• Tenure: The tenure of each manager (numeric).

• Level: The level in the corporate hierarchy (integer; 1 = CEO, 2 = Vice President, 3 = manager).

• Department: What department each manager is in (integer; 1, 2, 3, 4, or 0 for the CEO).

Details

Edges in the krack_advice and krack_friend networks come survey questions answered by all 21 managers. The krack_report network uses the formal organization chart to define connections between managers.

Source

The data was found at http://vlado.fmf.uni-lj.si/pub/networks/data/WaFa/default.htm and reformatted for use in R.

References

D. Krackhardt, Cognitive social structures. Social Networks. 9, 104 (1987). doi: 10.1016/0378-8733(87)90009-8

S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, 1994).

Make blockmodel objects using CONCOR partition

Description

Use the CONCOR algorithm to find network positions, continuing through a specified number of splits, and output blockmodel object(s).

Usage

make_blk(adj_list, nsplit = 1)

Arguments

Details

Runs concor to a specified number of splits (nsplit) and creates a blockmodel type object from each input matrix in adj_list using the membership vector generated by concor. This object holds summary information of interest, such as the reduced density matrix, as well as the permuted adjacency matrix that shows the blocked structure.

See the help file for blockmodel in the sna package for more details.

Value

A list of blockmodel type objects, one for each input adjacency matrix. Each blockmodel in the list corresponds to one relation.

See Also

blockmodel, concor

Examples

g1 <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(g1) <- c("a", "b", "c", "d")
colnames(g1) <- c("a", "b", "c", "d")

g2 <- matrix(c(0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0), ncol = 4)
rownames(g2) <- c("a", "b", "c", "d")
colnames(g2) <- c("a", "b", "c", "d")

gl <- list(g1, g2)
make_blk(gl)

Run CONCOR and output reduced adjacency matrices

Description

Takes a list of adjacency matrices, partitions using concor, and returns a list of reduced adjacency matrices and their corresponding cutoff densities. Each reduced matrix corresponds to one input relation. The sna package must be installed, but does not need to be attached.

Usage

make_reduced(adj_list, nsplit = 1)

Arguments

Details

A reduced network represents each identified position in the network as a single node. Links (or self-links) exist if the density of ties in that block is greater than a threshold density. In this implementation, the density of the whole network is used as the threshold for each block.

In the list of input matrices adj_list, each should correspond to a different relation for the same nodes. Each adjacency matrix is partitioned with the CONCOR algorithm, continuing for nsplit divisions. After the threshold density is applied, each entry in the reduced matrix has values of 0 or 1.

Value

References

S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, 1994).

See Also

concor, make_blk

Examples

g1 <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(g1) <- c("a", "b", "c", "d")
colnames(g1) <- c("a", "b", "c", "d")

g2 <- matrix(c(0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0), ncol = 4)
rownames(g2) <- c("a", "b", "c", "d")
colnames(g2) <- c("a", "b", "c", "d")

make_reduced(list(g1, g2), nsplit = 1)

Build an igraph object for a reduced network

Description

Turns a reduced adjacency matrix (usually output from make_reduced) into an igraph object. This function requires igraph to work.

Usage

make_reduced_igraph(reduced_mat)

Arguments

Value

A directed and unweighted igraph object for the reduced matrix.

See Also

make_reduced

Examples

a <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(a) <- c("a", "b", "c", "d")
colnames(a) <- c("a", "b", "c", "d")

r_mat <- make_reduced(list(a), nsplit = 1)
make_reduced_igraph(r_mat$reduced_mat[[1]])

Plot a blockmodel

Description

Displays a plot of a blockmodel. Based on plot.blockmodel (sna must be installed), but reformats the plot to be square and removes the mandatory title.

Usage

plot_blk(x, labels = FALSE, ...)

Arguments

Details

This is a modification of the plot.blockmodel function. The original displays vertex ids as row, column, and diagonal labels, which can be unreadable for larger networks. plot.blockmodel also adds a title of the form "Relation - 1", which this version omits.

Value

Returns NULL, invisibly.

Author(s)

Carter T. Butts (buttsc@uci.edu)

Modified by Tyme Suda

References

Carter T. Butts (2019). sna: Tools for Social Network Analysis. R package version 2.5. https://CRAN.R-project.org/package=sna

See Also

plot.blockmodel

Examples

g1 <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(g1) <- c("a", "b", "c", "d")
colnames(g1) <- c("a", "b", "c", "d")

gl <- list(g1)
bm <- make_blk(gl, 1)[[1]]
plot_blk(bm)

Plot a reduced network

Description

Plot a reduced network using igraph, with nodes colored by block number.

Usage

plot_reduced(iobject)

Arguments

Details

Plots the reduced network, where each node represents all the nodes assigned to that position by CONCOR. Node colors on the reduced network plot are assigned by position, so if CONCOR is also used for vertex color on a sociogram (as in plot_socio), the node colors will align between the plots.

Value

Returns NULL, invisibly.

See Also

make_reduced, make_reduced_igraph, plot_socio

Examples

library(igraph)
g1 <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(g1) <- c("a", "b", "c", "d")
colnames(g1) <- c("a", "b", "c", "d")

r_mat <- make_reduced(list(g1), nsplit = 1)
r_igraph <- make_reduced_igraph(r_mat$reduced_mat[[1]])

plot_reduced(r_igraph)

Plot sociogram colored by CONCOR partition

Description

Plots a network of interest using CONCOR partition as vertex color. Uses an igraph object, normally created by concor_make_igraph or concor_igraph_apply.

Usage

plot_socio(iobject, nsplit = NULL)

Arguments

Details

This is a shortcut to plot an igraph object with usually-readable settings. It looks for the input iobject to have a vertex attribute called csplit(nsplit) that holds the CONCOR partition assignment (for example, if nsplit = 2, then plot_socio expects a vertex attribute named csplit2).

Value

Returns NULL, invisibly.

See Also

concor, concor_make_igraph, concor_igraph_apply

Examples

a <- matrix(c(0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0), ncol = 4)
rownames(a) <- c("a", "b", "c", "d")
colnames(a) <- c("a", "b", "c", "d")

i_out <- concor_make_igraph(list(a))
plot_socio(i_out[[1]], 1)