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().
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_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_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