`nwbrokerage`

Gould-Fernandez brokerage roles

Syntax

nwbrokerage
[netlist]
,
group(varname)
[generate(newvarname)
replace
silent]


`group(varname)`	Existing Stata variable holding each node’s group membership (required)
`generate(newvarname)`	Required. Stem for the 5 new Stata variables that store role counts
`replace`	Replace existing variables
`silent`	Suppress display of results

Description

nwbrokerage counts, for every node b, how often it plays each of the five brokerage roles defined by Gould and Fernandez (1989). For every directed two-path a -> b -> c (with a != c) through b in which a and c are not tied (no tie a -> c; two-paths that a could skip because it reaches c directly are not counted, as in Gould and Fernandez), the role is determined by comparing the group membership of a, b and c (from group()):

coordinatora, b and c all in the same group
gatekeepera in a different group from b; c in the same group as b
representativea in the same group as b; c in a different group
consultanta and c in the same group, different from b’s
liaisona, b and c all in different groups

generate() is required and gives the stem for five new Stata variables, one per role, each holding node b’s count of that role (e.g. generate(_broker) produces _broker_coordinator, _broker_gatekeeper, _broker_representative, _broker_consultant and _broker_liaison).

For a directed network, a ranges over b’s incoming ties and c over its outgoing ties - brokerage is fundamentally about a reaching c through b. For an undirected network, incoming and outgoing ties are identical, so a and c both range over b’s (undirected) neighbors - the same five-role classification still applies, just without the directional distinction a directed network provides.

Examples

. nwwebuse florentine, nwclear
. gen faction = mod(_n, 2)
. nwbrokerage flomarriage, group(faction) generate(_broker)

Supported network types

Binary: yes. Directed: yes, and directionality is used directly (see Description) - this is the network type the model was originally defined for. Undirected networks are supported too, with the directional distinction collapsing away as described above. Weighted: not used - only the presence/absence of a tie determines whether a two-path exists; tie strength does not affect role counts. Signed: not checked. Two-mode: same as for the bipartite graph read as a one-mode network (valid; no mode-specific normalisation). group() must be an existing numeric Stata variable (a string variable is refused; use encode first) already aligned with the network’s nodes (the same convention nwmodularity’s own group() option uses) - nwbrokerage does not detect groups itself; pair it with nwconcor, nwcoreperiphery, nwcommunity, or a substantive attribute for the grouping.

Stored results

Scalars

r(pairs) total number of a-b-c two-paths counted, summed across all nodes and all five roles

References

Gould, R.V., Fernandez, R.M. (1989). Structures of mediation: A formal approach to brokerage in transaction networks. Sociological Methodology 19, 89-126.

nwbrokerage