Motifs of network brokerage

net_x_brokerage() returns the Gould-Fernandez brokerage roles in a network.

net_x_brokerage(.data, membership, standardized = FALSE)

Arguments

.data

A network object of class stocnet, igraph, tbl_graph, network, or similar. Internally any of these will be coerced to an efficient implementation. For more information on possible coercions, see e.g. manynet::as_stocnet().

membership

A character string naming an existing node attribute in the network, or a categorical vector of the same length as the number of nodes in the network where each element indicates the group membership of the corresponding node. While this may often be a vector created using node_in_*() functions, it can be any character vector that assigns nodes to groups or categories.

standardized

Logical scalar. Where TRUE, the counts are returned as z-scores against a null model rather than as raw counts. This is a different quantity from normalized, which divides by a theoretical maximum, and from scaled, which divides by the observed maximum: a z-score says how far the count departs from what the null model expects, so it can be negative and has no fixed range. By default FALSE.

Value

A network_motif named numeric vector or sometimes a data frame with one row and a column for each motif type, giving the count of each motif in the network. This is printed as a tibble to avoid greedy printing of long vectors.

Cognitive social structures

A cognitive social structure records each node's report of the ties in the whole network, in a by column that names who reported each tie. Counting every report as a tie of its own would count each tie once for every perceiver who reports it. So the functions here first combine the reports into the locally aggregated structure of Krackhardt (1987), with the intersection rule: a tie exists if both of its ends report it, and a message says so. A tie that names no reporter is kept as it is.

A tie-level function still returns one value for each report, so that the result can be added back to the network it was given. Each report takes the value of the tie that it reports. A report of a tie that is not in the aggregated structure takes NA, or FALSE for a mark. tie_is_random() is the exception, and draws among the reports.

To combine the reports in a different way, do this before the function, e.g. with manynet::to_aggregated(over = "by").

Krackhardt, David. 1987. "Cognitive social structures". Social Networks 9(2): 109-134. doi:10.1016/0378-8733(87)90009-8

See also

Other brokerage: measure_broker_node, measure_broker_tie, measure_brokerage, member_brokerage, motif_brokerage_node

Other motifs: motif_brokerage_node, motif_clique, motif_composition, motif_exposure, motif_hazard, motif_hierarchy, motif_homophily, motif_net, motif_node, motif_path, motif_periods

Examples

net_x_brokerage(ison_networkers, "Discipline")
#> # A tibble: 1 × 6
#>   Coordinator Itinerant Gatekeeper Representative Liaison Total
#>         <dbl>     <dbl>      <dbl>          <dbl>   <dbl> <dbl>
#> 1         385       463        498            548     703  2597