Core-periphery structure — core

Core-periphery model of Borgatti and Everett (2000): a group of nodes that are connected among themselves and with the rest, and a periphery of nodes that are connected with the core but not with each other.

Usage

core_periphery(
  A,
  method = c("discrete", "continuous"),
  digraph = FALSE,
  rep = 50
)

Arguments

A: A square matrix
method: Whether to return a discrete partition (default) or continuous coreness scores
digraph: Whether the matrix is directed or undirected
rep: Number of random partitions used to start the search, besides the one given by the degree of the nodes

Value

This function returns the fit of the model, and the partition or the coreness scores.

Details

The discrete model looks for the partition of the nodes into a core and a periphery that maximises the correlation between the observed matrix and the ideal pattern, where a tie is expected when at least one of the two nodes belongs to the core. The search starts from the nodes sorted by degree, and from rep random partitions, and then moves one node at a time while the correlation improves. As the search can end in a local optimum, the result of the random starts depends on the seed.

The continuous model gives each node a coreness score instead of a class. The scores maximise the correlation between the observed matrix and the products of the scores of each pair, and are given by the leading eigenvector of the matrix.

References

Borgatti, S. P. and Everett, M. G. (2000). Models of core/periphery structures. Social Networks, 21(4), 375–395. doi:10.1016/S0378-8733(99)00019-2

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 1, 1, 0,
  1, 0, 1, 1, 0, 1,
  1, 1, 0, 1, 0, 0,
  1, 1, 1, 0, 0, 0,
  1, 0, 0, 0, 0, 0,
  0, 1, 0, 0, 0, 0
), byrow = TRUE, ncol = 6)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)

core_periphery(A)
#> $fit
#> [1] 0.6000992
#> 
#> $core
#> [1] "a" "b"
#> 
#> $periphery
#> [1] "c" "d" "e" "f"
#> 
#> $class
#> [1] "core"      "core"      "periphery" "periphery" "periphery" "periphery"
#> 
core_periphery(A, method = "continuous")
#> $fit
#> [1] 0.7804686
#> 
#> $coreness
#>         a         b         c         d         e         f 
#> 0.5058703 0.5058703 0.4674790 0.4674790 0.1598706 0.1598706 
#>