Motifs of network hierarchy

net_x_hierarchy() collects the measures of hierarchy into a single motif, which can be used to compare the relative hierarchy of different networks. The measures of hierarchy are:

• net_by_connectedness() measures the proportion of dyads in the network that are reachable to one another, or the degree to which network is a single component.

• net_by_efficiency() measures the Krackhardt efficiency score.

• net_by_upperbound() measures the Krackhardt (least) upper bound score.

• net_by_reciprocity() measures the proportion of ties in the network that are reciprocated, which is a measure of the degree to which the network is non-hierarchical.

net_x_hierarchy(.data)

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().

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

References

On hierarchy

Krackhardt, David. 1994. Graph theoretical dimensions of informal organizations. In Carley and Prietula (eds) Computational Organizational Theory, Hillsdale, NJ: Lawrence Erlbaum Associates. Pp. 89-111.

Everett, Martin, and David Krackhardt. 2012. “A second look at Krackhardt's graph theoretical dimensions of informal organizations.” Social Networks, 34: 159-163. doi:10.1016/j.socnet.2011.10.006

See also

Other hierarchy: measure_hierarchy

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

Examples

net_x_hierarchy(ison_networkers)
#> # A tibble: 1 × 4
#>   Connectedness InvReciprocity Efficiency LeastUpperBound
#>           <dbl>          <dbl>      <dbl>           <dbl>
#> 1             1          0.209      0.574               1