`nwnclan`

Maximal n-clan enumeration

Syntax

nwnclan
[netlist]
[,
n(int)
generate(newvarname)
replace
minsize(int)
silent]


`n(int)`	Maximum geodesic distance allowed between any two members; default = 2
`generate(newvarname)`	Required. Name of the Stata variable that stores each node’s largest maximal-n-clan membership size
`replace`	Replace existing variable
`minsize(int)`	Smallest n-clan size to report; default = 3
`silent`	Suppress display of results

Description

nwnclan enumerates every maximal n-clan (Mokken 1979) in the network(s) in netlist - an n-clique (see that command for the base concept and n(int)) that additionally requires every pair of its own members to be reachable from one another while staying inside the group, within n(int) steps. An ordinary n-clique only guarantees each pair’s shortest path in the whole network is within n(int) - that path may run through a node that is not itself one of the n-clique’s own members, a known limitation of the plain n-clique concept (Alba 1973). n-clans fix exactly that: every member must be able to reach every other member using only paths that never leave the group.

nwnclan works by first enumerating every maximal n-clique (the same computation nwnclique itself performs) and then keeping only the ones whose own induced subgraph - built from the original network, restricted to just that n-clique’s members - has every pair of members within n(int) steps of each other, using only ties between members. This matches the standard treatment of n-clans in the literature: a maximal n-clique that fails this check is simply not reported as a clan at all, rather than being replaced with some smaller, clan-qualifying subset of itself - a genuine, deliberate limitation of the concept, not a shortcut taken here. Every n-clan is therefore also an n-clique, but not every n-clique is an n-clan; on a network with no “shortcut” structure (e.g. a network where every node’s shortest paths to everyone else already stay within whatever locally-dense region it belongs to) the two coincide exactly.

Like n-cliques, n-clans genuinely overlap, so nwnclan follows nwnclique’s own output shape: a single per-node “largest maximal n-clan membership size” summary variable (generate(newvarname), required), plus the complete overlapping structure in r(nclan_matrix) and r(nclans). minsize(int) defaults to 3, matching nwclique/nwnclique.

Examples

. nwwebuse florentine, nwclear
. nwnclan flomarriage, generate(_nclannum)
. nwnclan flomarriage, n(3) generate(_nclannum) replace

Supported network types

Binary: yes. Directed: yes, automatically symmetrized (same reasoning nwnclique already applies). Weighted: not used for membership. Signed: not checked. Two-mode: not checked. Inherits nwnclique’s own worst-case exponential enumeration cost, plus an additional per-candidate induced-subgraph diameter check - fine for the moderate network sizes typical of SNA datasets.

Stored results

Scalars

r(nclans) number of maximal n-clans found meeting minsize(int)

Matrices

r(nclan_matrix) n-clans-by-nodes 0/1 membership matrix, one row per maximal n-clan

References

Mokken, R.J. (1979). Cliques, clubs and clans. Quality and Quantity 13(2), 161-173.

Alba, R.D. (1973). A graph-theoretic definition of a sociometric clique. Journal of Mathematical Sociology 3(1), 113-126.

Wasserman, S., Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press. (cliques and cohesive subgroups)

nwnclan