`nwcoreperiphery`

Discrete core-periphery detection

Syntax

nwcoreperiphery
[netlist]
[,
generate(newvarname)
replace
measure(string)
maxiter(int)
silent]


`generate(newvarname)`	Required. Name of the Stata variable that stores core membership
`replace`	Replace existing variable
`measure(binary\\|valued)`	Whether to use tie values (valued) or only presence/absence of ties (binary); default = valued for valued networks, binary otherwise
`maxiter(int)`	Maximum number of local-search sweeps before giving up on convergence; default = 100
`silent`	Suppress display of results

Description

nwcoreperiphery partitions the nodes of a network into a “core” and a “periphery” using the discrete core-periphery model (Borgatti and Everett 1999). The core-periphery model assumes ties are expected between any pair of nodes where at least one is a core member (core-core and core-periphery ties are both structurally expected), while periphery-periphery ties are not expected at all. nwcoreperiphery searches for the 0/1 assignment (0 = periphery, 1 = core) whose implied pattern correlates as highly as possible with the network actually observed, starting from a degree-based seed and then repeatedly trying to flip each node’s status in turn, keeping any flip that improves the correlation, until a full sweep produces no further improvement. This is a greedy local search, not an exhaustive search over all 2^n possible partitions, so it can settle on a good but not necessarily globally optimal partition - the same character of algorithm nwcommunity already uses for modularity maximization.

generate() is required and names the new variable which stores, for each node, 1 if it was assigned to the core and 0 if it was assigned to the periphery.

Always operates on the undirected version of the network (the classical model does not distinguish incoming from outgoing ties); a directed network is symmetrized automatically, matching nwcommunity’s own convention - no separate symmetrize option is needed or offered.

Examples

. nwwebuse florentine, nwclear
. nwcoreperiphery flomarriage, generate(_core)

Supported network types

Binary: yes. Directed: yes, automatically symmetrized (no explicit symmetrize option, unlike nwcommunity - the model itself does not distinguish direction). Weighted: measure(valued) uses tie weights directly when computing the fitness correlation; measure(binary) uses presence/absence only; default follows the network’s own weighted-ness, matching nwcommunity’s convention. Signed: not checked. Two-mode: not checked - operates on the network’s own square adjacency matrix. A network with no ties at all is rejected explicitly (there is no structure to fit a core-periphery pattern to); a node with no ties of its own (an isolate) is handled without error and is simply assigned to the periphery.

Stored results

Scalars

r(fitness) correlation between the observed network and the ideal pattern implied by the found partition (-1 to 1; 1 = a perfect discrete core-periphery structure)
r(core) number of nodes assigned to the core

References

Borgatti, S.P., Everett, M.G. (1999). Models of core/periphery structures. Social Networks 21(4), 375-395.

nwcoreperiphery