concor {concorR}

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

m_list

A list of adjacency matrices. Matrices must be square, of the same dimensions, and have row/column names (node names). Each matrix represents a different relationship of the same nodes. If there is only one relationship of interest, m_list is a list of that single matrix.

nsplit

The number of times the input matrices will be partitioned. Each split divides a partition in two, resulting in 2^nsplit roles identified.

self_ties

A Boolean representing whether self-ties can be present in the data. TRUE allows for self-ties; FALSE does not.

cutoff

The cutoff point of the iterated correlations. Both this and max_iter can be lowered slightly to improve speed.

max_iter

The maximum number of times the correlation will be run for a split. Both this and cutoff can be lowered slightly to improve speed.

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))