Coordinator brokerage (Gould and Fernandez 1989) counts the open two-paths \(a \to v \to c\) through node \(v\) in which \(a\), \(v\) and \(c\) all belong to the same group. A two-path is open when the network has no edge from \(a\) to \(c\). This role is \(w_I\) in the notation of the source.
Arguments
- x
Network input accepted by
centrality.- membership
Group labels, one per node.
- ...
Further arguments to
centrality, such asnormalized.
Value
A named integer vector with one count per node, in input node
order. normalized = TRUE returns a numeric vector.
Details
The measure is defined for directed networks. On an undirected network it
returns NA with a cograph_undefined_measure warning, and the
same happens when membership is missing, where the warning also has
class cograph_bad_membership. A membership whose length
differs from the number of nodes raises a cograph_bad_membership
error. Group labels may be numbers
or strings. Edge weights and self-loops are ignored. The other four roles
are centrality_brokerage_itinerant,
centrality_brokerage_representative,
centrality_brokerage_gatekeeper and
centrality_brokerage_liaison.
References
Gould, R. V., & Fernandez, R. M. (1989). Structures of mediation: A formal approach to brokerage in transaction networks. Sociological Methodology, 19, 89-126. doi:10.2307/270949 .
Examples
centrality_brokerage_coordinator(regulation_net, membership = rep(1:2, each = 5))
#> Explore Plan Monitor Adapt Reflect Discuss Synthesize
#> 1 0 2 1 1 0 0
#> Evaluate Create Share
#> 0 2 0