core_periphery: Detect Core-Periphery Structure

In cograph: Analysis and Visualization of Complex Networks

Detect Core-Periphery Structure

Description

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

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.

Value

A data frame with class "cograph_core_periphery" and columns node, role, and coreness. Fitness, core density, periphery density, and the original network are stored as attributes.

References

Borgatti, S.P. & Everett, M.G. (2000). Models of core/periphery structures. Social Networks, 21(4), 375-395. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0378-8733(99)00019-2")}

See Also

centrality, network_summary

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

# Discrete assignment
cp_disc <- cograph::core_periphery(adj, method = "discrete")
cp_disc$assignment

cograph documentation built on May 31, 2026, 5:06 p.m.