`nwkcore`

k-core decomposition

Syntax

nwkcore
[netlist]
[,
generate(newvarname)
replace
silent]


`generate(newvarname)`	Required. Name of the Stata variable that stores each node’s coreness
`replace`	Replace existing variable
`silent`	Suppress display of results

Description

nwkcore computes the k-core decomposition (Seidman 1983) of a network or a list of networks. A node’s coreness is the largest k such that the node belongs to a k-core: a maximal subgraph in which every node has degree at least k within that subgraph. Nodes with high coreness sit in the network’s densely interconnected “core”; nodes with low coreness (e.g. degree-1 pendants) sit on the periphery. Coreness is a common building block for identifying cohesive subgroups and for network visualization (e.g. sizing/coloring nodes by coreness, or restricting a plot to the k-core for some threshold k).

All calculations are performed on the undirected version of the network: for directed networks, a node’s neighbor set is the union of its out- and in-neighbors, matching how nwcomponents treats directed networks for the same kind of undirected-sense structural question.

generate() is required and names the new variable which stores each node’s coreness.

Examples

. nwwebuse florentine, nwclear
. nwkcore flomarriage, generate(_kcore)
. tab _kcore

Supported network types

Binary: yes (only) - coreness is a structural property, tie values are ignored. Directed: yes - each node’s neighbor set is the union of its out- and in-neighbors (matching nwcomponents’s own weak-connectivity convention and nwsimindex’s identical choice), not symmetrized distances. Weighted: not applicable. Signed: not applicable. Two-mode: not checked.

Stored results

Scalars

r(maxcore) maximum coreness found (the network’s degeneracy)

Matrices

r(core_sizeid) distribution over coreness levels

References

Seidman, S.B. (1983). Network structure and minimum degree. Social Networks 5(3), 269-287.

Batagelj, V., Zaversnik, M. (2003). An O(m) Algorithm for Cores Decomposition of Networks. arXiv:cs/0310049.

nwkcore