Identifies core-periphery structure in a network with a continuous (Borgatti-Everett) or a discrete method. Core nodes are densely interconnected, and periphery nodes connect mainly to the core. Edge weights are ignored; the analysis uses the binary adjacency matrix.
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 power iterations. Must be at least
Default 100.
- digits
Integer or NULL. Number of decimal places for the coreness scores, the fitness and the densities. Default NULL (no rounding).
- ...
Passed to
to_igraph, which accepts no further arguments. Any argument supplied here raises an error.
Value
A data frame with class "cograph_core_periphery", one row per
node, and columns:
- node
Node label.
- role
Character:
"core"or"periphery". For the continuous method a node is core when its coreness is at or above the median coreness.- coreness
Numeric continuous coreness score, rescaled to \([0, 1]\). Reported for both methods.
The attributes "fitness", "core_density" and
"periphery_density" hold the fit and the block densities, and
"network" holds the original input.
Details
Continuous method
The Borgatti-Everett model compares the adjacency matrix with the rank-1
pattern matrix outer(c, c) of a coreness vector c. Here
c is estimated from the dominant eigenvector of the adjacency
matrix, refined by power iteration with rescaling to \([0, 1]\). The
iteration stops when the largest change falls below \(10^{-6}\) or after
iter steps. The vector is not optimized for the correlation. The
"fitness" attribute is the correlation between the off-diagonal
entries of the adjacency matrix and those of the pattern matrix (the lower
triangle for a symmetric matrix), and it is 0 when the correlation is
undefined.
Discrete method
The discrete method starts from the continuous solution split at the median
and repeatedly flips the single node assignment that most increases
density(core) - density(periphery). It stops when no flip increases
this quantity. The "fitness" attribute is the correlation between the
adjacency matrix and the ideal block pattern of the final assignment.
Printing and plotting
Printing the result shows the core and periphery sizes, the fitness and the
two block densities, followed by the node table. The result is a data frame
and serves as the tidy table directly. plot() on the result is
documented in plot-results.
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(regulation_net)
#> Core-Periphery | Core: 5 Periphery: 5 Fitness: 0.030
#> Core density: 0.350 | Periphery density: 0.350
#>
#> node role coreness
#> Explore periphery 0.07985633
#> Plan core 1.00000000
#> Monitor periphery 0.00000000
#> Adapt core 0.44368868
#> Reflect periphery 0.17972217
#> Discuss periphery 0.05077436
#> Synthesize core 0.39000808
#> Evaluate periphery 0.12894782
#> Create core 0.72952631
#> Share core 0.51706359