`nw2clustering`

Clustering coefficient (transitivity) of a two-mode network

Syntax

nw2clustering
[netname]
[,
measure(string)
level(int)
generate(newvarname)
replace]


`measure(binary\\|arithmetic\\|geometric\\|maximum\\|minimum)`	How to combine a 4-path’s own four tie values; binary dichotomizes every tie to presence/absence first; arithmetic/geometric/maximum/minimum combine the four raw tie values via that function; default = arithmetic for a valued network, binary otherwise
`level(int)`	Which mode (1 or 2) to compute clustering scores for; default = 1
`generate(newvarname)`	Required. Name of the Stata variable that stores each `level()`-mode node’s own clustering coefficient
`replace`	Overwrite an existing `generate(newvarname)` variable; required if it already exists
`ra`	The global clustering coefficient of Robins and Alexander (2004), 4 C4 / L3 (C4 the number of four-cycles, L3 the number of paths of length three) of the binary network; `generate()` is then optional; results in `r(ra)`, `r(C4)`, `r(L3)`

Description

nw2clustering is the form of nwclustering for a two-mode network: nwclustering uses it by default on a two-mode network (and onemode forces the one-mode coefficient). The two names give the same result with the same options.

nw2clustering calculates the two-mode (bipartite) analogue of the ordinary clustering coefficient (see nwclustering) using the 4-path / 6-cycle definition of Opsahl (2013) and Robins & Alexander (2004): an ordinary triangle cannot exist in a two-mode network (a tie only ever connects the two different modes), so “closure” is instead measured on paths of length 4 - two level()-mode nodes connected via two distinct intermediate opposite-mode alters - and a path is closed when its two ends are ALSO both tied to some further common alter, forming a 6-cycle. This deliberately excludes shorter 4-cycles (reusing one of the same two alters) as a form of closure, matching the cited reference’s own distinction between mere shared-affiliation redundancy and genuine triadic-style closure.

Only nodes of the requested level() receive a value; nodes of the other mode are left missing. A node with too few alters, or whose own connected component has fewer than 3 same-mode nodes, has no possible 4-path and its own coefficient is reported missing (not spuriously 0).

nwclustering automatically switches to this command whenever it is called on a two-mode network, forwarding measure() and generate() (always at the default level(1) in that case) - call nw2clustering directly to choose level(2) or a non-default measure().

Examples

. nwset ego alter, twomode name(bip)
. nw2clustering bip, generate(_clustering2_lev1)
. sum _clustering2_lev1

Supported network types

Binary: yes (the default measure(binary) case). Directed: not checked - a two-mode network’s ties are treated as undirected. Weighted: yes, via measure(arithmetic|geometric|maximum|minimum), each combining the 4-path’s own four tie values before testing closure. Signed: not checked; negative tie values are not validated or rejected. Two-mode: yes - the clustering coefficient of Opsahl (2013), four-paths closed by a fifth tie (as tnet::clustering_tm); ra adds the global coefficient of Robins and Alexander (2004), 4 C4 / L3.

Stored results

Scalars

r(C_avg) mean of the per-node clustering coefficients (the requested level() only)
r(C_global) network-level global clustering coefficient (ratio of total closed to total
potential 4-paths)

Macros

r(measure) the measure() actually used

References

Opsahl, T. (2013). Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Social Networks 35(2), 159-167.

Robins, G., Alexander, M. (2004). Small worlds among interlocking directors: Network structure and distance in bipartite graphs. Computational & Mathematical Organization Theory 10(1), 69-94.

nw2clustering