`nwnclan`

Maximal n-clan enumeration

Syntax

nwnclan
[netlist]
[,
n(int)
generate(newvarname)
replace
minsize(int)
maxcliques(#)
maxtime(#)
countonly
nomatrix
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
`maxcliques(#)`	Stop with an error when more than this many maximal n-cliques have to be examined while looking for n-clans; default = 1,000,000
`maxtime(#)`	Stop with an error when the search has run for this many seconds without finishing; default = 60
`countonly`	Only count the sets (and tabulate them by size) - nothing is stored, so the count is not limited by memory; `generate(newvarname)` is then not needed
`nomatrix`	Do not build the sets-by-nodes matrix; the `generate(newvarname)` variable and the count are still returned
`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: same as for the bipartite graph read as a one-mode network (valid; no mode-specific normalisation). Inherits nwnclique’s own worst-case exponential enumeration cost, plus an additional per-candidate induced-subgraph diameter check.

Stored results

Scalars

r(nclans) number of maximal n-clans found meeting minsize(int)
r(maxsize) size of the largest set (with countonly or nomatrix)

Matrices

r(size_table) (with countonly or nomatrix) sizes and the number of sets of each size
r(nclan_matrix) n-clans-by-nodes 0/1 membership matrix, one row per maximal n-clan (not with countonly or nomatrix)

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