These functions, together with net_reciprocity(), are used jointly to
measure how hierarchical a network is:
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_connectedness(.data)
net_by_efficiency(.data)
net_by_upperbound(.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().
A network_measure numeric score.
The object also carries the measure it computed, the range its values
can fall within, and whether and how those values were normalized.
These are shown as a one-line header when the object is printed.
Where a measure offers a choice between several ways of counting the
same thing, it also carries the variant it used.
All can be retrieved with attr().
For signed networks, these measures consider only the positive ties,
and say so.
They read a tie as a distance, and a negative tie is hostility
rather than a channel along which cohesion travels.
Use manynet::to_unsigned() first to control this yourself.
A perfect hierarchy is a tree: every node but the root has exactly one superior, and there are no ties to spare. Krackhardt's efficiency asks how close a network comes to that, by counting the ties it carries in excess of the minimum needed to hold its components together, as a proportion of the most excess ties it could possibly carry: $$E = 1 - \frac{|E| - \sum_i (N_i - 1)}{\sum_i \left(M_i - (N_i - 1)\right)}$$ where \(N_i\) is the size of weak component \(i\) and \(M_i\) the number of ties possible within it. A tree or forest scores 1, and a complete network 0.
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
Other measures:
measure_accuracy_net,
measure_accuracy_node,
measure_assort_net,
measure_assort_node,
measure_breadth,
measure_broker_node,
measure_broker_tie,
measure_brokerage,
measure_central_between,
measure_central_close,
measure_central_degree,
measure_central_eigen,
measure_central_tie_between,
measure_central_tie_close,
measure_central_tie_degree,
measure_central_tie_eigen,
measure_closure,
measure_closure_node,
measure_cohesion,
measure_core,
measure_diffusion_infection,
measure_diffusion_net,
measure_diffusion_node,
measure_diverse_net,
measure_diverse_node,
measure_diverse_tie,
measure_features,
measure_fit,
measure_fragmentation,
measure_periods
Other hierarchy:
motif_hierarchy
net_by_connectedness(ison_networkers)
#> # Connectedness, normalized [0, 1]
#> [1] 1
1 - net_by_reciprocity(ison_networkers)
#> # Reciprocity, normalized [0, 1]
#> [1] 0.209
net_by_efficiency(ison_networkers)
#> # Efficiency, normalized [0, 1]
#> [1] 0.574
net_by_upperbound(ison_networkers)
#> # Least upper boundedness, normalized [0, 1]
#> [1] 1