Brokerage roles

Counts, for each node v, the two-paths i -> v -> j with i != j and no tie i -> j (v brokers between them), by the roles of Gould and Fernandez (1989), given each node's group: coord (coordinator: i, v and j in one group), itin (itinerant: i and j in one group, v in another), repr (representative: v in i's group, j outside), gate (gatekeeper: v in j's group, i outside) and liais (liaison: three groups). Undirected, each tie runs both ways, so each unordered pair of neighbours counts twice and repr equals gate. Weights are not taken. Graph rules as in ntdeg(). Raw counts only: the expected counts and z-scores of Gould and Fernandez are not given.

Usage

ntbrk(from, to, grp, nodes = NULL, dir = FALSE)

Arguments

from, to

Labels of the two ends of each edge: vectors of the same length (zero when nodes gives every node) with no missing values.

grp

The group of each node: labels, named by node or one per node in node order, as memb in ntmod().

nodes

NULL, or every node's label once: the node order of the results and the way to include isolated nodes.

dir

TRUE for a directed graph (from sends a tie to to).

Value

A data frame: node, grp (as text), coord, itin, repr, gate, liais and total.

References

Gould, R. V. and 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

ntbrk(c("a", "b", "b"), c("b", "c", "d"),
      grp = c(a = "x", b = "y", c = "y", d = "z"), dir = TRUE)
#>   node grp coord itin repr gate liais total
#> 1    a   x     0    0    0    0     0     0
#> 2    b   y     0    0    0    1     1     2
#> 3    c   y     0    0    0    0     0     0
#> 4    d   z     0    0    0    0     0     0