Identifies core-periphery structure in a network using either continuous (Borgatti-Everett) or discrete methods. Core nodes are densely interconnected, while periphery nodes connect primarily to the core.
Usage
core_periphery(
x,
method = c("continuous", "discrete"),
directed = NULL,
iter = 100,
digits = NULL,
...
)Arguments
- x
Network input: matrix, igraph, network, cograph_network, or tna object
- method
Character string; either "continuous" (default, Borgatti-Everett model) or "discrete" (binary core/periphery assignment).
- directed
Logical or NULL. If NULL (default), auto-detect from matrix symmetry. Set TRUE to force directed, FALSE to force undirected.
- iter
Integer; maximum number of iterations for the continuous algorithm. Default 100.
- digits
Integer or NULL. Round numeric outputs to this many decimal places. Default NULL (no rounding).
- ...
Additional arguments passed to
to_igraph
Value
A list with class "cograph_core_periphery" containing:
- scores
Named numeric vector of continuous coreness scores (0 = periphery, 1 = core)
- assignment
Named character vector of "core" or "periphery" labels
- fitness
Correlation between adjacency matrix and ideal core-periphery pattern
- core_density
Edge density within the core subgraph
- periphery_density
Edge density within the periphery subgraph
Details
Continuous method (Borgatti-Everett):
Finds a coreness vector c (values 0-1) that maximizes the correlation
between the adjacency matrix and the ideal rank-1 pattern matrix
(the outer product of the coreness vector with itself). The algorithm
initializes from eigenvector centrality and iteratively refines via
power iteration until convergence.
Discrete method: Produces a binary core (1) / periphery (0) assignment. Starts from the continuous solution, thresholds at the median, then greedily swaps node assignments to maximize fitness. Discrete fitness is defined by high density within the core and low density within the periphery.
References
Borgatti, S.P. & Everett, M.G. (2000). Models of core/periphery structures. Social Networks, 21(4), 375-395. doi:10.1016/S0378-8733(99)00019-2
Examples
# Core-periphery in a simple network
adj <- matrix(c(
0, 1, 1, 1, 0,
1, 0, 1, 1, 0,
1, 1, 0, 1, 1,
1, 1, 1, 0, 1,
0, 0, 1, 1, 0
), 5, 5)
rownames(adj) <- colnames(adj) <- LETTERS[1:5]
cp <- cograph::core_periphery(adj)
cp
#> Core-Periphery | Core: 4 Periphery: 1 Fitness: 0.569
#> Core density: 1.000 | Periphery density: 0.000
#>
#> node role coreness
#> A core 0.6504481
#> B core 0.6504481
#> C core 1.0000000
#> D core 1.0000000
#> E periphery 0.0000000
# Discrete assignment
cp_disc <- cograph::core_periphery(adj, method = "discrete")
cp_disc$assignment
#> NULL